Site Application of a Channel Network Model for Groundwater Flow and Transport in Crystalline Rock

Transkript

1 Examensarbete vid Institutionen för geovetenskaper Degree Project at the Department of Earth Sciences ISSN Nr 436 Site Application of a Channel Network Model for Groundwater Flow and Transport in Crystalline Rock Applicering av en flödesvägsmodell på ett specifikt fältområde för grundvattenflöde och transport Jonas Pedersen INSTITUTIONEN FÖR GEOVETENSKAPER DEPARTMENT OF EARTH SCIENCES

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3 Examensarbete vid Institutionen för geovetenskaper Degree Project at the Department of Earth Sciences ISSN Nr 436 Site Application of a Channel Network Model for Groundwater Flow and Transport in Crystalline Rock Applicering av en flödesvägsmodell på ett specifikt fältområde för grundvattenflöde och transport Jonas Pedersen

4 ISSN Copyright Jonas Pedersen Published at Department of Earth Sciences, Uppsala University ( Uppsala, 2018

5 Abstract Site Application of a Channel Network Model for Groundwater Flow and Transport in Crystalline Rock Jonas Pedersen Groundwater flow and transport in deep crystalline rock is an important area of research. This is partly due to its relevance for constructing a long term repository for storing radioactive spent nuclear fuel in deep bedrock. Understanding the behavior of flow and transport processes in deep crystalline rock is crucial in developing a sustainable solution to this problem. This study aims to increase the understanding of how channel network models (CNM) can be applied to represent groundwater flow and solute transport in sparsely fractured crystalline rock under site specific conditions. A main objective was to determine how to incorporate structural and hydrogeological site characterization data in the construction of the CNMs. In addition to this, the associated key parameters of the CNMs were investigated to gain further understanding of model site application. To that end, a scripting approach with the python scripting library Pychan3d was used to create alternative channel network representations of a field site. A conceptual discrete fracture network (DFN) model was constructed using field site data obtained from a structural model of the fractures present at the site of the Tracer Retention Understanding Experiments (TRUE) - Block Scale at the Äspö Hard Rock Laboratory (HRL). This conceptual model was used as a base for constructing two different alternatives, denoted respectively as sparse and dense, of a CNM. The sparse CNM consisted of a limited amount of channels for each fracture, while the dense CNM acted as a DFN proxy, taking the full extent of the fracture areas into account and creating a dense, large network of flow channels for each fracture. In order to verify the performance of the generated CNMs, a reproduction of tracer tests performed at the same specific field site was attempted using a particle tracking technique. In addition to this, long term predictions of solute transport without the interference of the pumps used during the tracer tests were done in order to estimate transport time distributions. Pychan3d and the scripting approach was successfully used to create CNMs respecting specific conditions from the TRUE-Block Scale site. The sparse CNM was found to give very adequate flow and transport responses in most cases and to be relatively easier to calibrate than its dense counterpart. The long term transport predictions at the site according to the models seem to follow a channelized pattern, with only a few select paths for transport. The difficulties encountered in matching the dense CNM with the tracer tests most likely stem from difficulties in flow calibration, as well as certain key parameters being assigned too generically. Keywords: channel network models, discrete fracture networks, model calibration, groundwater flow and transport Degree Project E1 in Earth Science, 1GV025, 30 credits Supervisor: Benoît Dessirier Department of Earth Sciences, Uppsala University, Villavägen 16, SE Uppsala ( ISSN , Examensarbete vid Institutionen för geovetenskaper, No. 436, 2018 The whole document is available at

6 Populärvetenskaplig sammanfattning Applicering av en flödesvägsmodell på ett specifikt fältområde för grundvattenflöde och transport Jonas Pedersen Grundvattenflöde och transport av kemikalier i kristallin berggrund är ett viktigt nutida forskningsområde. Detta beror till stor del på dess relevans för konstruktionen av ett långtidsförvar för radioaktivt kärnavfall. Att förstå flödes och transportprocesser i kristallin berggrund är en viktig del i att utveckla en hållbar lösning för detta problemet. Den här studien syftar till att öka förståelsen för hur modeller som representerar flödesvägar i kristallin berggrund kan användas för att samla information angående grundvattenflöde och transport av kemikalier. Ett huvudsyfte med detta var att undersöka vilka versioner av den här modelltypen som bäst representerar platsspecifik strukturell och hydrogeologisk data, samt förmågan att använda detta för att simulera grundvattenflöde och transport. För att kunna genomföra den här studien så användes Pychan3d, ett programmeringsbibliotek till programmeringsspråket Python. Alla modeller skapade i studien gjordes genom egenskriven kod i Python 3 som använde sig av Pychan3d för att generera modeller. En konceptuell modell skapades över ett specifikt fältområde utifrån strukturer och sprickzoner som tidigare hade karterats i föregående studier. Den konceptuella modellen användes som grund för att skapa två olika versioner av flödesvägsmodeller. Den ena modellversionen bestod av ett fåtal flödeskanaler per sprickzon medans den andra versionen istället bestod av en stor mängd flödeskanaler. Detta representerade två olika teorier om hur flödesvägar för kristallin berggrund kan se ut. Dessa modeller verifierades med hjälp av spårämnesförsök, där en vald kemikalie injiceras och återhämtas för att testa hypoteser kring bland annat flödesvägar. Utöver detta gjordes långsiktiga förutsägelser angående flödesvägarna för fältområdet för att uppskatta hur grundvattenflödet ser ut i ett orört system. Pychan3d användes på ett framgångsrikt sätt för att skapa en konceptuell model samt flödesvägsmodeller för området. Modellversionen med färre flödeskanaler per sprickzon genererade bättre resultat än sin motpart, och visade sig även vara lättare att kalibrera för fältområdet. Resultat av de långsiktiga förutsägelserna visade att flödet i området följer ett mycket begränsat antal flödesvägar. Svårigheterna för den andra modellversionen att generera likvärdiga resultat grundar sig troligtvis i svårigheter med kalibrering, samt att vissa egenskaper hos modellen ansågs vara för generaliserade. Nyckelord: grundvattenmodellering, kristallin berggrund, modellkalibrering, fältspecifik studie Examensarbete E1 i geovetenskap, 1GV025, 30 hp Handledare: Benoît Dessirier Uppsala universitet, Villavägen 16, Uppsala ( ISSN , Examensarbete vid Institutionen för geovetenskaper, Nr 436, 2018 Hela publikationen finns tillgänglig på

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8 Table of figures Figure 1. Structural model of the fractures identified in the TRUE Block Scale characterization volume (Figure reproduced from Hermansson and Doe, 2000)... 6 Figure 2. The polygons representing fracture structures visualized in a 3d space through Paraview, each color represents a different fracture. Top-down view on the left, bottom-up view on the right Figure 3. The added borehole lines in green over the partially shaded fracture structures, surrounded by the boundary box Figure 4. Channel geometry parameters Figure 5. Cacas channel generation method used for the sparse CNM Figure 6. The structure of the generated sparse CNM, calculated conductance shown in the channels Figure 7. Triangulated mesh network of flow channels Figure 8. The generated mesh for the dense CNM. Conductances are visible for the channels Figure 9. The injection and sink sections, displaying the different flow paths in green used by the tracer tests (Figure reproduced and adapted from Andersson et al., 2001) Figure 10. The layers of the different rock types adjacent to a fracture (Mahmoudzadeh et al., 2013) 21 Figure 11. The injection curves of tracers used for the tracer tests (Figure reproduced from Andersson et al., 2001) Figure 12. Comparison of calibration values obtained by the different CNMs Figure 13. Final version of the sparse CNM, boreholes in green, fractures in grey and the channel network with hydraulic head shown in color scale Figure 14. Final version of the dense CNM, boreholes in green and the channel network with hydraulic head shown in color scale Figure 15. Results for the reproduction of tracer tests by the sparse and dense CNM. The points represent the target recovery times for the tests Figure 16. Sparse CNM with particle exit nodes enlarged, particle injection node is shown in green. 32 Figure 17. The sparse CNM particle exit nodes with their respective exit fracture Figure 18. Dense CNM with particle exit nodes enlarged, particle injection node is shown in green. 33 Figure 19. The dense CNM particle exit nodes with their respective exit fracture Figure 20. Leakage scenario prediction particle recovery time Figure 21. Dense CNM fracture 21 head field, with the sink section notable in deep purple... 37

9 Table of contents 1. Introduction Introduction of the research subject Background and site description Äspö Hard rock laboratory TRUE Block Scale Aim Methodology and data management Conceptual model construction Pychan3d description Introduction of Pychan3d Steady state flow solution Sparse channel network model creation Dense channel network model creation Tracer tests, transport simulation Transport simulation model Tracer test Simulation Canister leakage scenario prediction Results First comparison of channel networks Comparison of tracer tests reproduction Sparse channel network model Dense channel network model Canister leakage scenario prediction Discussion Pychan3d and scripting approach Recovery rates Flow path impact on the transport simulations Calibration impact Leakage Scenario prediction Uncertainty discussion Future work Conclusions Acknowledgements Reference list Appendix Appendix Python code Defining and creating a DFN Sparse CNM creation... 51

10 Table of contents (continued) Dense CNM creation Sparse CNM calibration and adding of channels Dense CNM calibration and adding of channels Interpolation of head values Sparse CNM transport simulation tracer tests Dense CNM transport simulation tracer tests Sparse CNM Leakage scenario transport simulation Dense CNM Leakage Scenario transport simulation... 60

11 1. Introduction 1.1 Introduction of the research subject Flow and transport in fractured rock is an important and active area of research (Berkowitz, 2002; Figueiredo et al., 2016), in part due to current research in several countries regarding the development of a nuclear waste repository in deep crystalline bedrock. The idea behind the safety of a nuclear radioactive waste repository is based on a concept of multiple barriers for protection. This includes a canister containing radioactive waste, which is surrounded by a buffer that encloses the canister from the surrounding medium. This is then surrounded by a geological barrier of crystalline bedrock to minimize the potential risk of transporting radionuclides into the biosphere (Tsang et al., 2015). The storage of this canister and its potential leakage risk is a main reason why it is of interest to understand the processes governing groundwater flow and transport in fractured crystalline rock. The flow of water in fractured crystalline rock is often highly dominated by paths of least resistance embedded in connected rock fractures, which results in a sparse network of channels concentrating the majority of the flow, a phenomenon known as channeling. (Tsang and Neretnieks, 1998). Accounting for this channeling effect in numerical models for flow and transport is not straightforward. Difficulties include the characterization of the population of flowing fractures in the rock mass of interest (either by deterministic and/or stochastic methods) and the development of a conceptual model for in-plane channeling, both of which require geometrical and hydraulic parameters. The characterization of the fractures is complex because it is difficult to directly observe them inside the rock, which is further complicated by the high level of heterogeneity present in fractured rock (Figueiredo et al., 2016). There are different approaches to modelling flow in fractured rock. Two of them are the Discrete Fracture Network (DFN) models and Channel Network Models (CNM) (Figueiredo et al., 2016). DFN models explicitly represent fractures, with given position, orientation, length, aperture and transmissivity. Field investigations such as borehole logging, outcrop mapping and pumping tests are used to infer fracture orientation, trace length and transmissivity distributions. These are used to create a fracture network which respects the statistical properties and geometry of the fractures that could be observed at the field site. The parallel plate model is often used either in 2D with lines or in 3D with planar polygons to describe flow in the fractures. This approach assumes a constant aperture in each fracture (Hyman et al., 2015). One drawback of the DFN approach is the need for a large and quite detailed input data set. The model in itself is also very demanding in regards to computation power, an effect of the large amount of data used (Long et al., 1982). The CNM emphasizes the fact that flow and transport in fractured rock usually occur primarily along flow channels and it usually allows to use semi-analytical flow solutions, which significantly reduces the computational burden. 1

12 It is generally easy to create CNMs in a generic way assuming regular channel arrangements, e.g. fully populated or randomized cubic lattices (Figueiredo et al., 2016). However, the lattice spacing and the generation rules used to build and populate these channel models are somewhat arbitrary and hard to directly relate to the available field data. This is especially true when building a site-specific model that should conform to deterministic features. To bridge this gap, there is a need to design and test flexible methodologies to build channel networks based on features identified during site characterization and observed fracture statistics. In other words, to find ways to simplify DFN-realizations honoring the distributions of geological rock fractures observed in the field, into hydraulic channel networks that allow fast scoping calculations. A distinction can be made between geological/mechanical fracture networks (or geodfn) that are conceptual and geometric models of all the fractures in the rock and channel networks that are conceptual models for flow and transport. A geodfn can easily include the main fractures identified during site characterization and can often reproduce the observed background fracture statistics very realistically. The geodfn can also be used as the base for the creation of a hydrogeological DFN flow model (or hydrodfn) by taking all or only a subset of the fractures to define a flow network. The difficulty here lies in the fact that only a small fraction of all observed fractures are found to deliver measurable groundwater flows, which makes the translation of a geodfn into a hydrodfn a complex task. This approach to creating a flow model has been attempted (e.g Hartley et al., 2007), but was found to lead to large models that are cumbersome and difficult to use at the characterization stage (Andersson et al., 2002). In this study an alternative way to use the geodfn to build a channel network for flow and transport will be explored. The link between the hydrodfn, the geodfn and the channel network approach is that the flow channels of the channel network are contained inside the same fracture network, but not all of the fracture surfaces are open and subject to flow. Instead, the channel model focuses on a few channels in order to simulate the channeling effect. Different versions of CNMs can be hypothesized and built based on the same geometry of the geodfn and this study will focus on a couple of simple algorithms to generate channel networks from a fracture network. 1.2 Background and site description This project is based on the work undertaken in the Tracer Retention Understanding Experiments (TRUE) Block Scale project done at the Äspö Hard Rock Laboratory (HRL), in south eastern Sweden Äspö Hard rock laboratory The Äspö hard rock laboratory (HRL) is located in south eastern Sweden on the Baltic coast and was constructed by the Swedish Nuclear Fuel and Waste Management Company (SKB) in order to conduct research regarding the storage of spent nuclear fuel in deep bedrock. The project of building the Äspö 2

13 HRL started in 1986, and finished after an extensive site characterization process in 1995 when the 3600 meter long tunnel had reached its target depth of 450 meters into the bedrock (Stanfors et al., 1999). The geology of the area around the laboratory is characterized and dominated by granitoids from the Trans- Scandinavian Igneous Belt (Kornfält et al., 1997; Stanfors et al., 1999). This crystalline bedrock is one of the reasons why this area is of interest for SKB, as the target bedrock for the spent nuclear fuel repository is also crystalline TRUE Block Scale The project was active from 1996 until 2002 and subdivided in several stages. The main objectives of the TRUE Block Scale project were to increase our knowledge regarding tracer transport in a fractured rock mass, evaluate the importance of diffusion and sorption mechanisms as well as estimating the connection between transport and flow data and its role in predicting transport events (Andersson et al., 2002). One task the TRUE Block Scale study undertook was to characterize a rock volume in order to be able to perform tracer tests in a defined space of bedrock fractures. The rock volume was characterized as a 200x250x100 meter cubic shape, forming the basis for where these tracer tests could be conducted. This consisted of first identifying hydraulic structures within the rock volume selected for the project. In order to identify and find out how these structures were connected, five cored boreholes were drilled combined with pressure responses. The identification process was done by combining pressure responses from drilling with drilling records, in order to confirm locations of existent fractures. This procedure gave a general outline of how the fractures were structured and connected inside the rock volume (Andersson et al., 2002). After this the fractures were verified with the help of flow logging techniques. The rock mass volume established in the TRUE study is the target volume used as field site specific conditions in this master s thesis. The TRUE Block Scale project report obtained a wide range of field data, some of which was used for this thesis. All coordinates imported and used were in Easting Northing of the Äspö relative coordinate system (Andersson et al., 2002). 1.3 Aim The idea for this project is to use field site data from the Äspö Hard Rock Laboratory to create a sitespecific conceptual 3D DFN model. After this has been done the conceptual DFN model will be downscaled to two different versions of a channel network model by proposing new sets of rules. These two alternative models, sparse channel network and dense channel network based on DFN characteristics, will then be compared against each other as well as with the field site data. The aim of this is to try to determine how to efficiently apply a channel network model to a field site, and further 3

14 investigating which parts of the field data can be incorporated in the channel network design, help site characterization and reduce the uncertainty of model predictions. Thus, the aim of this study is to further increase the understanding of how channel network models can be applied to site specific conditions, while investigating how these models are influenced by their parameters. This will be done by using the Pychan3d scripting library to create a conceptual model which will be used in order to create a sparse CNM and a dense CNM. The sparse CNM will consist of a limited amount of channels for each fracture, while the dense CNM will act as a proxy to a full discrete fracture network (DFN) representation. The differences between the two different model versions will then be compared in order to test our confidence in the alternative conceptual models for flow and in each case understand the role of the main model parameters. All of the models created and simulations undertaken in this study were performed by a scripting approach written in Python 3, which allowed for a large degree of freedom for the work conducted in this study. The questions that this study aims to answer are: How can a scripting approach be applied to site specific conditions and be used for the creation of corresponding flexible channel networks? How well can the groundwater flow and transport processes in a fractured crystalline rock mass at the Äspö HRL be simulated by a sparse CNM and a dense CNM respectively? To what degree are the two CNMs influenced by their respective parameters, and in what ways do the models differ in regards to calibration? 4

15 2. Methodology and data management This method section starts with a description of how the conceptual model for the fractures located in the TRUE Block Scale area at the Äspö HRL was created. After this there is a short introduction of the python scripting library Pychan3d, and how it is applied in this thesis. The conceptual model is then used in order to create two different CNMs. The first model is based on the concept that the flow of the fractures behaves according to the channeling effect, which means that the flow chooses paths of least resistance and forms preferred pathways for fracture flow. This effect is represented through a sparse channel network, with merely a few number of channels present for each fracture. The second model on the other hand takes all of the geometrical properties of the fractures into account, and is based on the concept of discrete fracture network models. This yields a denser channel network, with a large number of channels present, incorporating the entire structure of the fractures. In addition to this, tracer tests which are used both to calibrate the CNMs and as target values for transport simulations are introduced. Additionally, in this step the transport simulation solving of Pychan3d is explained. The obtaining of data and the calculations of parameters for the tracer tests are explained, and the different flow paths used are introduced. Finally, a flow simulation concerning the outcome of a leaking radioactive canister scenario is introduced and explained, as a final means of comparing the two alternative CNMs. 2.1 Conceptual model construction The first step of this project was creating a conceptual model for the fractures present in the rock domain, as well as determining the extent of the rock volume that was to be used for the study. Hermansson and Doe (2000) constructed a structural model of the fractures within the TRUE Block Scale site. The structural model was done in order to obtain the necessary geological knowledge for further development of models for the TRUE Block Scale project. The structural model is shown below in figure 1 which gives a 2-D overview seen as a horizontal cut of the fractures that are going to be used in the model, with corresponding number identification for each fracture. 5

16 Figure 1. Structural model of the fractures identified in the TRUE Block Scale characterization volume (Figure reproduced from Hermansson and Doe, 2000) Dershowitz et al. (2003) conducted a study investigating the main hydraulically conductive structures at the Äspö HRL. This was performed as a preparatory work for model development in future projects at the Äspö hard rock laboratory. From this report, data was obtained representing transmissivity, storativity and transport aperture for the fractures, as well as coordinates for the fracture corners. The different models presented below are all based on the data obtained by Dershowitz et al. (2003). Using coordinates representing the corners of the fractures obtained by Dershowitz et al. (2003), polygons could be created representing the known fracture structures. The general outline and shape of the fractures can be seen below in figure 2. These polygons were then used to define where the fractures intersect with one another. 6

17 Figure 2. The polygons representing fracture structures visualized in a 3d space through Paraview, each color represents a different fracture. Top-down view on the left, bottom-up view on the right. Through this, the fracture intersections were located; these play an important part in defining the channel network later on. In addition to this, five boreholes which had been used during the TRUE block scale project were selected and reconstructed. The borehole/fracture intersections were mentioned in Andersson et al. (2002), but information such as coordinates of location and direction was not available. This had to be collected from (Nordqvist et al., 2008) instead, where data consisting of the coordinates where the boreholes intersected two fractures (19 and 20), and the total drilled length of the boreholes was obtained. These were then constructed using the direction of each borehole together with the maximum depth and length of the boreholes. The coordinates were used to obtain the direction of the boreholes, and the start and end coordinates of the boreholes were calculated using simple vector algebra. The boreholes were important to include for several reasons; firstly it gave a clearer picture of what section of the rock volume would be critical to include in the rock volume block for the channel model. Secondly, the boreholes intersections with fractures were used as injection and pump locations of tracer tests performed in the TRUE project. These tracer tests were later reproduced in order to compare the channel network models with the actual field site data. Using this information, the extent of the rock volume that would be used for the models could be determined, and a block shaped boundary box was constructed around the components (fracture polygons, boreholes and fracture intersections). This can be seen below in figure 3, where the boreholes are also visible as lines, in green. The size of the boundary box was constrained by being large enough to not be directly influenced by the model boundaries and incorporating the core elements of the fracture network, while still not being too large to manage. It is notable that the fracture seen closest to the top of figure 2 (fracture 5) has been cropped to a size that better fit the boundary box. This was necessary to avoid this very large fracture from wrongly influencing the model as the fracture s relative size was much larger than the constructed boundary condition box. 7

18 Figure 3. The added borehole lines in green over the partially shaded fracture structures, surrounded by the boundary box. Pychan3d uses differences in hydraulic head in the network to model the flow direction and velocity. In order to simulate this, hydraulic head boundary conditions had to be obtained. Hydraulic head values were obtained in the TRUE project through interpolation from other borehole pressures around the TRUE rock mass (Dershowitz et al., 2003). In order to obtain head values for the target rock mass these values were imported as a table containing the hydraulic head values at specific known coordinates for the rock volume (Dershowitz et al., 2003). These values had been produced during the preparatory work for the TRUE block scale project. The head value coordinate data was used to interpolate the head values at boundary conditions of the defined rock volume. This was done with the help of the python module Scipy (Oliphant, 2007) griddata, a module which interpolates unstructured D-dimensional data. This module simply takes the known coordinates with their respective head values and uses the known data in order to interpolate values at new positions inside a created grid network. The interpolation method used was the nearest neighbor method, which selects the value of the nearest point and assigns it for the newly generated node. The boundary condition positions where the new head values were interpolated were decided from where 8

19 the fractures intersected with the established boundary box, where every fracture/boundary intersection was designated as a head boundary condition. Through this, a set of head boundary condition nodes were obtained which were used for solving the steady state flow. In order to solve the steady state flow, a first version of the channel network was constructed using assumptions about the network structure (sparse or dense) and the conductances based on the geometry of the generated channels in the network. In addition to this, to link the channel network to the surrounding bedrock an estimation was made of the boundary exchange terms. This is represented by the hydraulic head boundary condition nodes generated through the interpolation process. Using the conductance channel network together with the boundary conditions the steady state flow could be solved for the channel network. The generated flow solution was then used to simulate transport for the tracer test reproductions. In the construction of the CNMs used in this study, the python scripting library Pychan3d was used for solving two problems, the steady state flow and the solute transport simulation. The next chapter shortly introduces Pychan3d, the conceptualization of a channel and its parameters, and how Pychan3d is used to solve the steady state flow problem. The solute transport simulation problem is explained at a later stage, in combination with the tracer test characteristics. For a more detailed and rigorous description of Pychan3d and its structure, the reader is referred to the paper covering the development of Pychan3d (Dessirier et al., 2018). 2.2 Pychan3d description Introduction of Pychan3d This section introduces the Pychan3d scripting library, describes the structure of a flow channel, and explains how Pychan3d was used for solving the steady state flow. Pychan3d is a python scripting library for creating channel models with the capability to model flow and transport, developed by Dessirier et al. (2018). Pychan3d is developed as a package for Python, with dependencies on the python modules Numpy (Oliphant, 2006) and Scipy (Oliphant, 2007), this allows for easy portability and a fast code development (Dessirier et al., 2018). Furthermore, in Pychan3d a scripting approach is used, which entails that the user builds a script in order to create the desired outcome. This approach has the advantage of preserving an explicit record of the modelling process, together with greatly decreasing the time needed for developing the package. This avoids the massive work that developing and maintaining a graphical user interface would entail (Dessirier et al., 2018). Additonally, Pychan3d provides the option to easily export channel networks and their flow solutions in vtk format which provides a fast and simple way of visualizing and supervising the output created through scripts in Pychan3d (Dessirier et al., 2018). This is done through the external open source software Paraview. 9

20 The visualization capabilities of Pychan3d proved to be a very useful tool for evaluating and investigating the generated results. It added a concrete viewpoint of the conceptual models in an otherwise very abstract workflow. The option to review the generated models in a 3D environment constituted a critical step during the calibration process of the different stages of model creation. All of the figures in this study that display the different models are screenshots taken from Paraview, this also demonstrates the versatility of visualization that is present in this software. The scripting approach of Pychan3d was used for the generation of the conceptual models together with the channel networks. The code used in this study was written in Python 3 in Anaconda Jupyter Notebook (Kluyver et al., 2016). Jupyter Notebook is a python programming software which allows you to divide your code into code blocks that can be run separately in an interactive computational environment. This significantly helps with structuring code, demonstrating computation segments step by step and providing a pedagogic and user friendly work environment. The code for the project was structured into a multitude of notebook files, covering the different features and models created during the study. The python code written and used for the major steps of the method is included and shown in the appendix Steady state flow solution A channel can be conceptualized as a long opening with a constant aperture and cross-section (see figure 4). In that case the flow of a channel between two intersections of channels can be described by its conductance C. The conductance is a parameter which combines the effects of the channels average hydraulic conductivity K and its geometry. The geometry is expressed by the cross sectional area A and length L of the channels. The cross sectional area A is obtained by the width (w) multiplied by the aperture (b) of the channels. The conductance can then be expressed as (Moreno and Neretnieks, 1993): C = K wb L The flow rate which is present in the specific channel can after this be calculated by Darcy s law: Q = C Δh (2) (1) Figure 4. Channel geometry parameters Where C is the calculated conductance of the channel and Δh the difference in hydraulic head between the end nodes of the channel. In order to define the steady state flow problem for the entire channel network, it is necessary to know its topology. The topology of the network can be defined as the structure of the network and how the channels in the network are connected. Other important aspects include the conductance for the channels as well as the boundary conditions present in the channel network. 10

21 Therefore from a mathematical point of view, a channel network can be represented by a flow graph where the nodes of the graph are the channel intersections and the edges of the graph are the channels of the network which are characterized by their conductance (Li et al., 2014). In order to solve the flow problem, one needs to solve a sparse system: M h = b (3) Where h is the vector of unknown heads at the channel intersections, M is a symmetric positive definite matrix which is the Laplacian matrix of the conductance graph, with the generic term: (m ij) i j = C ij (4) (m ij) = j C ij + δ Dirichlet,i C bnd (5) Where C ij is the conductance of a channel between the nodes I and j, δ Dirichlet,i is an indicator function which is equal to 1 at nodes which have a fixed head boundary condition assigned to them, and to 0 elsewhere. C bnd is an arbitrary constant with a value which is considerably larger than all conductance values of the system, and b is a sparse vector of boundary conditions which has the general form: b i = δ Dirichlet,i C bnd h bnd,i + δ Neuman,i q bnd,i (6) Where δ Neuman,i is an indicator function for nodes with a prescribed flow boundary condition, h bnd,i and q bnd,i are head and flow values, which are applied at the boundaries as boundary conditions. From this graph representation it is clear that the lattice topology which has been used by previous channel networks such as Moreno and Neretnieks, (1993) is one way to generate and parameterize stochastic networks, but it is not necessarily a needed assumption to include in order to create graph representations of channel networks. 2.3 Sparse channel network model creation The first approach to generating a channel network model was influenced by the methodology used in Cacas et al., (1990). This approach was taken in order to be able to simulate the so called channeling effect of the fracture flow paths. Flow channels forming the channel network model were generated with certain prerequisites. Channels were generated from every fracture center, connecting with nodes representing fracture/boundary intersections and fracture intersections. In addition to this, a group of channels were manually added between fracture centers and borehole/fracture intersections which were needed for later calibration. This created a sparse network of channels representing the flow paths of the fractures present in the rock volume. Figure 5 below shows the results of Cacas method for fracture 10, with boundary intersections occurring at the top, west and bottom nodes, a fracture intersection with fracture 19 at node 14, and the red dot representing an intersection with borehole KI0023B. 11

22 Figure 5. Cacas channel generation method used for the sparse CNM While this figure shows the automated process of the Cacas method, further steps were taken in order to make the flow network into an adequate representation of the network of fractures. For the later calibration process, the flow values of certain borehole/fracture intersections were used as target values. In order to incorporate these nodes representing the intersection points, the channel network had to be modified to include the corresponding nodes. As can be seen in figure 5, the borehole/fracture intersection is represented by node 58, located between node 38 and 15. The thought process that went behind the modification of the channel network was that the necessary intersection nodes should be included without changing the structure of the network in any significant way. Using fracture 10 as an example of including the intersection node, this would have been done by first removing the automatically generated channel between nodes 38 and 15, and then adding channels between node 38 and 58 together with a channel between node 58 and 15. This made the channel take a slight detour and incorporate the previously left out borehole intersection. The method was verified by visualization of the resulting new network in Paraview, making sure that all of the corresponding borehole/fracture intersections were accounted for. Figure 6 shows the structure of the generated sparse channel network as visualized through Paraview, with every line representing a channel. As can be seen, the middle section of the boundary box is where the largest clusters of channels are present, an effect of the large amount of fractures present in that section. 12

23 Figure 6. The structure of the generated sparse CNM, calculated conductance shown in the channels The next part included the calibration process of the sparse channel network model. The first approach to this was done by using a table of ambient flow values obtained from Andersson et al. (2000). This table contained the ambient flow values of a select number of intersection points between boreholes and fractures, and is reproduced in table 1 below. The ambient flow refers to the state of the flow system without the influence of a local pump or injection in the model domain. For these flow field measurements, the main head gradient that drives the flow was dominated by the large scale hydraulic structures together with the presence of the nearby Äspö HRL tunnel which was continuously drained (Andersson et al., 2000). These flow values were then used as a target profile in order to obtain corresponding values for the borehole intersection nodes present in the channel network model. This was done through manual calibration. Firstly, the steady state flow of the channel network model was solved, giving a first set of results to calibrate from. These values were compared with the flow values of nodes from the channel network representing the borehole intersections, termed as node throughflow values. Changes that could be made manually to the network through the script included adding new flow channels and modifying the conductance of already existing channels in order to fit the flow values better. After the first comparison was done and in order to obtain a better fit, new 13

24 channels were added manually, the conductance of specific channels was modified, then the steady flow state was solved again, allowing for a new comparison with the flow values from Andersson et al. (2000). As an example from the calibration process, one of the most impactful calibration steps was the addition of a short circuit channel between fracture 6 and 20. As can be seen in table 1, the flow rate for these two borehole/fracture intersections are significantly higher than the other flow values reported. The cause for this according to Andersson et al. (1999) was the presence of a short circuit between the two fractures via an open section of one borehole, which dramatically increased the flow rate. Since Cacas method did not take this short-circuit channel into account during the automatic channel network construction, this needed to be fixed manually. A high conductance channel was added between fracture 6 and 20, in order to represent the short circuit between the two fractures. The flow values from Andersson et al. (1999) compared to the final calibrated values are shown below in table 1. At most the values between the two tables differed by one order of magnitude in either direction, which was deemed adequate. The values obtained from Andersson et al. (2000) concerning fracture specific parameters are all based on a single value given to each different fracture. Since the sparse CNM is based on these values, but instead goes into finer detail using multiple channels for every fracture, it is reasonable that the values are not a perfect match. For a more graphical overview of the flow calibration values in table 1, see figure 12 in chapter 3.1. This figure gives a more relative comparison between the measured and calibrated values. Table 1. Ambient flow and calibration values for the sparse CNM Sparse Ambient flow Field data CNM Borehole Fracture Flow(m 3 s -1 ) Flow(m 3 s -1 ) KA2563A E E-07 KI0025F E E-07 KI0025F E E-08 KI0023B E E-07 KI0025F E E-07 KI0025F E E-09 KI0023B E E-09 KA2563A E E-08 KI0025F E E-08 KA2563A E E-08 KI0025F E E-09 KI0023B E E-07 KI0025F E E-08 KI0023B E E-06 KI0023B E E-06 14

25 2.4 Dense channel network model creation The second method of generating a CNM was influenced by the structure and approach of DFN models. A DFN model can be explained as a computational model, which represents all the geometrical features of fractures present in a fracture network. These geometrical features include parameters such as fracture orientation, position, aperture, shape and size (Lei et al., 2017). DFN models can be generated from several different methods, in this study we directly used the fractures described in the conceptual model of Hermansson and Doe (2000) as a deterministic DFN. As such, the DFN fracture polygons created in the conceptual model stage were also used for the creation of the dense channel network. The thought behind the dense CNM was that it would act like a DFN-proxy, representing the main characteristics and behavior of an actual DFN model while still using the same numerical tool for simplicity. This approach was taken in order to simulate the behavior of a very dense network of channels, and in order to create the other end of a spectrum when comparing to the sparse CNM. In figure 7 below, a fracture view of the generated triangulation mesh network is visualized. Figure 7. Triangulated mesh network of flow channels The channel network was generated by using the software GMSH, a free software finite element mesh generator developed with the intention of providing a fast and user friendly meshing program (Geuzaine and Remacle, 2009). GMSH was used to generate positions for a set of nodes over the fracture polygon planes, these points were then used to generate the mesh network using a Delaunay triangulation. The positioning of the nodes were set in such a way that they respected intersections of different fractures, as well as respecting the locations of borehole intersections into the fractures. Each side of the generated triangles constitute a flow channel for the corresponding fracture. The properties of the channels were calculated through Pychan3d using a set of uniform fracture wide parameters. In table 2 below the channel properties are listed together with the method used in obtaining them by the two channel models. 15

26 Table 2 : Channel geometrical properties Channel property Sparse CNM Dense CNM Length Euclidean distance Euclidean distance Tortuosity Estimated by calibration Estimated by calibration Width Estimated by calibration Calculated by pychan3d to respect the total area of each fracture Aperture Calculated with cubic law Calculated fracture aperture The boundary conditions were generated in a similar way as in Cacas network. For every channel that intercepted the boundary box a boundary condition node was created. When comparing to Cacas network, this naturally generated a large amount of boundary condition nodes. In the figure 8 below, the generated DFN channel network is shown. As can be seen, the size of the network is taking the full extent of the fracture plates into account, leading to a much larger area being used by the channel network. Figure 8. The generated mesh for the dense CNM. Conductances are visible for the channels. 16

27 The calibration process for the dense CNM was done in the same manner as Cacas network. The same flow values were used as the target values to obtain during calibration. As an effect of the many channels, adding single channels and increasing the conductance of certain channels had a very minor effect on the channel network. As such, the DFN based dense channel network was found to be difficult to calibrate, which lead to the flow target values for the borehole/fracture intersections being difficult to match. Another effect of this was that the short circuit between fracture 6 and 20 did not have as big of an effect for the dense CNM. Partially due to this, the flow values for the dense CNM were difficult to properly match several of the target values for the observed values. The ambient flow values together with the dense CNM calibration results are presented below in table 3. For a more graphical overview of the flow calibration values in table 3, see figure 12 in chapter 3.1. This figure gives a more relative comparison between the measured and calibrated values. Table 3. Ambient flow and calibration values for the dense CNM Ambient flow Field data Dense CNM Borehole Fracture Flow(m 3 s -1 ) Flow(m 3 s -1 ) KA2563A E E-07 KI0025F E E-07 KI0025F E E-08 KI0023B E E-08 KI0025F E E-08 KI0025F E E-08 KI0023B E E-08 KA2563A E E-08 KI0025F E E-09 KA2563A E E-07 KI0025F E E-07 KI0023B E E-07 KI0025F E E-08 KI0023B E E-07 KI0023B E E Tracer tests, transport simulation In order to verify how well the transport simulations of the models represent the actual field site data, tracer tests from test stage C of the TRUE block scale project were reproduced. The tracer tests were also used to calibrate the transport simulation results of Pychan3d. The original tests were carried out by Andersson et al. (2001) to increase the understanding of radionuclide retention in a specific fracture network. 17

28 This set of tests was chosen for reproduction as the tests were supported by a clear documentation of how the tests were performed and a good presentation of the results. This allowed for comparing the different results at a later stage. In the tests, three different flow paths were used for four different tracer injections; several different tracers were used for each test. While in the case of reproducing the tracer tests for this study, only one tracer was injected for each test. In figure 9 below, a 2D overview seen as a horizontal cut for the three injection points are shown together with the sink (pump out), displaying the three flow paths of the tracer tests. Figure 9. The injection and sink sections, displaying the different flow paths in green used by the tracer tests (Figure reproduced and adapted from Andersson et al., 2001) Flow path I was used by tracer tests C1 and C4, and goes from the injection point in fracture 20 to the sink point of fracture 21. It is characterized by the structural model as a fairly straight forward single flow channel, incorporating two different fractures. Flow path II was used in tracer test C2, and stretches from the injection point in fracture 23 to the sink of fracture 21. This flow path is instead a longer and more complex flow path, incorporating several fractures and plenty of network channels. It is therefore recognized as a network flow path. Flow path III was used in tracer test C3, with both the injection and sink points located in fracture 21. It is described by the structural model as a rather long, single flow channel path. 18

29 The tracer test field results were measured by a cumulative tracer recovery, with the time of 5, 50 and 95% mass recovery measured. In the case where a 95% recovey was not reached, the final recovery of the tracer test was used instead Transport simulation model In order to simulate the tracer tests from test section C, the transport model of Pychan3d was used. The transport model is based on a particle tracking technique, which tracks the transport of groundwater flow through a selected number of particles. The simulation of transport can be broken down into two parts, a mixing rule at each node and a model for transport in each channel. The simplest of mixing rules is the case of perfect mixing at every node, which would result in a hypothetical particle of solute leaving a node through a specific channel with a probability that is equal to the outflow rate of the channel divided by the total throughflow of the specific node (Berkowitz et al., 1994). This is the mixing rule that was used for the transport simulations used by the models in this thesis. As mentioned, each channel needs a model for its transport. The transport model takes into account and is thus dependent on the transport processes occurring within the channel. These are usually a function of the geometry of the channels, but can also be dependent on the structure and characteristics of the rock mass adjacent to the channel as well as the type of particle that is being transported (Dessirier et al., 2018). The transport model determines the travel time through the channels by a travel time probability distribution P(t) for the particle that is being transported. The transport model used for the modelling in this study accounted for the effect of advection, diffusion and sorption. However, the effect that dispersion might have on the transport in a single channel was not included due to modelling limitations. This entails that the particle is subject to advection along the channel opening, diffusion into the pores of the surrounding rock mass, and sorption on the surfaces and walls of the channels (Moreno and Neretnieks, 1993). The travel time distribution thus becomes: P(t) = FWS 2Q MPG P(t) = 0, for t R V Q exp ( π(t R V )3 Q ( FWS Q )2 MPG 2 4(t R V Q ) ), for t > R V Q where R is the surface retardation factor, V the volume of the channel, Q the flow rate of the channel, FWS is the flow wetted surface, which is the surface area of the channel in contact with flowing water. It can be expressed as a function of channel length and width: (7) (8) FWS = 2 L W (9) Finally, MPG stands for material property group, and describes the combined retardation that occurs as an effect of diffusion and sorption in the rock mass (Moreno and Neretnieks, 1993). Pychan3d and its transport model was used in order to solve the equations listed above. 19

30 As demonstrated in the text above, in order to solve the solute transport problem one needs several inputs. At a bare minimum, the channel volume is needed in order to calculate the advective travel time for a solute. By taking diffusion and sorption of the solute into account one also needs to include and know the FWS and MPG. In Pychan3d, transport is implemented as a particle tracking technique together with the injection of a predetermined amount of particles. Each injected particle can be assigned to a node as a transport starting point, either through a resident injection (uniformly) or through flux injection which is a flux-weighted rule (Dagan, 2017; Frampton and Cvetkovic, 2009; Kang et al., 2017). Resident injection is the injection of particles from a source at a given fixed rate, while flux injection is typical of a large source performing at a constant head (Dagan, 2017). In Pychan3d it is possible to use a piecewise linear concentration-time relationship for the tracer injection in order to assign an injection time to each particle, which can be a very useful tool for using injection profiles from field sites (Dessirier et al., 2018). The travel times of the channel segments used in Pychan3d are generated by a random sampling of the selected travel time distribution, which is based on the geometry of the channel as well as the adjacent rock parameters. The result of this is that each simulated particle is represented by an array of nodes representing where it has passed together with an array representing the corresponding times of passage. In addition to this, Pychan3d also includes routines to export the particles of the transport simulation as vtk files to Paraview which allows for a fast and simple visualization along with diagnostics of the particle transport and injection (Dessirier et al., 2018). In order to account for the different characteristics of the chosen tracers, the material property group (MPG) value had to be calculated for each tracer. The MPG is calculated through equation (10). MPG = D e K d ρ b (11) Where D e is the effective diffusivity of the tracer in the rock matrix, and K d ρ b is known as the rock capacity factor, and is equal to (Moreno and Crawford, 2009): K d ρ b = ε p + (1 ε p ) K d ρ s (12) where ε p is the matrix porosity, K d and K d are matrix sorption coefficients based on the bulk (ρ b and solid (ρ s ) densities. K d and K d differs in that K d also takes the storage capacity of the water filled rock matrix porosity into account. For non sorbing tracers, the variable K d ρ b can thus be estimated to be equal to the porosity, which simplifies the MPG equation to: MPG = D e ε p (13) D e is obtained by: D e = F t D w (14) where F t is formation factor, a constant which determines the impact from the porosity of the rock type on the diffusivity coefficient and D w is the diffusion coefficient of the tracer in water. 20

31 In order to account for the different rock types present in the flow paths, the distance that the tracer would flow through the rock mass was calculated by ((Mahmoudzadeh et al., 2013): i τ Df = (δ f i ) 2 D i (15) af i where τ Df is the time for a solute to diffuse through the ith layer of rock mass adjacent to the flow channel, (δ f i ) 2 i is the distance the tracer has traveled through diffusion and D af coefficient through the porous media, which is expressed as: is the diffusion i D af = D e ε where D e is the effective diffusivity of the tracer and ε is the porosity of the rock type. In Moreno and Crawford (2009), the properties of a fracture channel s geological structure in regards to its adjacent rock types was listed. This refers to the different geologic materials in the fracture plane, and their different equilibration times in regards to sorption and diffusion. In table 4 below, the rock types adjacent to the fractures are listed, with the distance from the fracture walls shown. These values were then used in order to solve equations above and estimate the MPG values for the tracers used, with regards to the diffusion distance traveled through rock by the tracer. In order to determine the impact of the rock type for tracer diffusion, the calculated distance was weighted against the extent of the rock types, giving the zone with the highest distance the most weight for the porosity and formation factor. Figure 10 gives an overview of the different rock layers that are adjacent to a fracture. (16) Figure 10. The layers of the different rock types adjacent to a fracture (Mahmoudzadeh et al., 2013) In order to estimate how much time would be needed to diffuse through each rock type layer, the extent length from the table was used as the distance (δ i f ) 2 in equation 15 above, this made it possible to determine which of the rock types from table 4 that should be included in the MPG calculation. 21

32 Table 4. The different rock types adjacent to a channel and their characteristic parameters (Moreno and Crawford, 2009) Rock type Extent (cm) Porosity % Formation Factor Intact wall rock E-05 Altered zone E-04 Cataclasite E-04 Fault gouge E-02 Fracture coating E-03 In addition to this, the results of the tracer tests were calibrated by changing the parameters of the channels such as their aperture, width and tortuosity. For the Cacas method, the cubic law was used to calculate the aperture for each channel present in the network, and in the case of the DFN method the hydraulic aperture was estimated uniformly for each fracture. While the hydraulic aperture is based on the cubic law for calculating the aperture, it is an approximation of the equation, which is used by Dershowitz et al. (2003). As the models constructed in this study is built upon the data collected through their study, it seemed reasonable to use the same approximation for calculating the aperture as they had. The cubic law used for the channel aperture is expressed as (Witherspoon et al., 1980): Q = ρg(12µ) 1 b 3 h (17) where Q is the discharge, ρ the fluid density, g the gravitational force, µ the viscosity of the fluid, b the aperture and h the hydraulic gradient. The flow is solved in order to obtain the corresponding apertures for the fractures. The hydraulic aperture e h, can be expressed as (Dershowitz et al., 2003): e h = a h T b h (18) where a and b are empirical constants and T transmissivity. The constants a h and b h are both equal to 0,5 which is based on the analysis made by Dershowitz et al. (2003). Using the transmissivity values obtained from Dershowitz et al. (2003) the hydraulic aperture of the fractures could be calculated. The next step in preparing the tracer test reproduction was the task of replicating the tracer injection concentration curve. In order to adequately copy the injection concentration of the tracers used in the tracer tests, the concentration-time relationship of the tracer injection curves from Andersson et al., (2001) were used. The corresponding concentration vs time values were imported into the Pychan3d script by approximating the injection curves for test C tracer tests shown below in figure 11. As mentioned in the Pychan3d chapter, the option of using a concentration-time relationship for the tracer injection is a great asset when using Pychan3d in the reproduction of tracer tests, and was consequently used here. 22

33 Figure 11. The injection curves of tracers used for the tracer tests (Figure reproduced from Andersson et al., 2001) Tracer test Simulation All of the tracer tests for the models were simulated with the same parameters and settings. The tracer tests were also under the influence of the borehole pump sink section. This caused a significant drop in pressure around the sink, influencing the groundwater flow to go towards this section. This also means that the influence of the previously mentioned tunnel sink can be considered close to negligible in this case due to the high rate of pumping used during the tracer tests. The injection and sink rates of the different tracer tests were represented in the models as flow boundary conditions nodes. The injection nodes were given a positive flow value to simulate the injection of fluid into the system, while the sink node was given a negative value to account for the pump extracting fluid from the system. In table 5 below the different parameters and their respective values for the different CNMs are listed. 23

34 Table 5. CNM parameters with respective values Parameter Sparse CNM Dense CNM Width 0.65m based on total fracture area Length Euclidean Euclidean Tortuosity Aperture Channel specific 10-4 m Fracture specific, between 10-4 m and 10-5 m Number of injected particles 30,000 30,000 For the transport simulations, perfect mixing at channel intersections was assumed for the solutes, the diffusion into the rock matrix and sorption was assumed to be one dimensional (perpendicularly to the fracture plane). The surface retardation factor, R, was set equal to 1, and the length of the channels were set to the Euclidian distance multiplied by a tortuosity factor (Table 5). For each simulation 30,000 particles were injected through a time-linear injection profile curve. The number of particles was chosen as it provided stable estimates of the times to specific mass recoveries. In the tracer tests performed by the channel models the simulation time was set to infinity in order to track all of the particles being injected. This expectedly had the effect of making all of the simulated tracer tests eventually reach a 100% mass recovery. Therefore, to compare the simulated tracer tests with the measured field observations, the 5, 50 and maximum percentage test recovery times were analyzed. The width and tortuosity of the channels were kept as constant as possible throughout the transport simulation of the tracer tests. The width simply represents the actual width of each separate channel, and a general estimation of 0.65m for each channel was used for this parameter in the case of the sparse channel network. The tortuosity is an expression of how straight the channels are.. The tortuosity is the ratio of the actual channel length over the straight distance between the channel extremities. As a consequence you get that a tortuosity value of 1 corresponds to a straight channel while a higher value indicates curves in the direction of the channel. Since a fracture network consisting solely of completely straight channels of flow seems an unlikely case, the tortuosity was given a value of 2.2 for the transport simulations, in order to simulate a more realistic scenario. The specific value of 2.2 was obtained through manual calibration and testing, through the process described in chapter 2.3 regarding calibration methods. Tracer test C1 Tracer test C1 had its injection through borehole KI0025F03, and goes from where borehole KI0025F03 intersects with fracture 20 onwards to the sink section at borehole KI0023B, fracture 21. This same sink section was used for all of the tracer tests. The tracer had an injection flow rate of 25 ml/min while the 24

35 sink had a significantly higher pump rate of 1950 ml/min at the sink section, this is also the pump rate used for all of the other tracer tests (Andersson et al., 2001). The tracer chosen to be reproduced for this test is an isotope of Bromide 82 Br -. Its diffusivity coefficient in water, D w, is 8.33*10-10 m 2 /s (Yuan-Hui and Gregory, 1974). Through this, the MPG value was calculated to be 5.00*10-7 m 2 /s. Tracer test C2 For tracer test C2, the injection node was the intersection point of borehole KI0025F03 and fracture 23, with an injection flow rate of 8.5 ml/min. The tracer reproduced for this test was a radioactive isotope of perhennate, 186 ReO 4-. The D w of ReO 4 was estimated to 1.46*10-9 m 2 /s ((Wu et al., 2014), this in turn gave an MPG value of 6.62*10-7 m 2 /s. Tracer test C3 For tracer test C3, the injection node was the intersection point of borehole KI0025F02 and fracture 21, with an injection flow rate of 1.8 ml/min. The reason for the relatively low injection rate was due to this injection being a passive injection without any kind of added flow. In comparison, all of the other tracer tests used in this study had a forced injection of flow which in turn increased the actual flow rate occurring in the channels naturally. The tracer targeted for reproduction from this test was HTO (tritiated water), with a D w value of 2.13*10-9 m 2 /s (Dershowitz et al., 2003) which gave the MPG value of 3.94*10-6 m 2 /s for HTO and tracer test C3. Tracer test C4 In tracer test C4, the flow path and thus the injection node was identical to test C1. The injection flow rate was also the same, with 25ml/min. What was different were the tracers used and their injection curves. The tracer chosen for reproduction in for this test was a radioactive isotope of Iodide, 131 I -. The D w value for 131 I - was determined to be 2.00*10-9 m 2 /s (Dershowitz et al., 2003), which gave an MPG value of 7.75*10-7 m 2 /s. 2.6 Canister leakage scenario prediction In addition to the tracer test reproductions, a particle tracking simulation was performed with the established CNMs, but without the tracer test specific flow boundary nodes. This reverted the flow influence back to that of a tunnel influenced hydraulic gradient over the field site, as the borehole pump section was no longer active. A scenario such as this is interesting since it can be performed to help predict the outcome of a canister leaking radioactive waste into the bedrock system. This can potentially be used to gain further insight in how a leakage scenario of radionuclides could behave in a fractured crystalline rock mass. 25

36 In this case, a particle simulation was generated at the injection node of flow path III, at the intersection of borehole KI0025F02 and fracture 21. This was done to investigate how the flow travels through the system without the interference of the massive pump section otherwise active in the tracer tests. This was done in order to make a long term prediction of solute transport, to estimate transport time distributions in a situation close to an active deposition tunnel. For the tracer test reproductions, the pump rate of 1950 ml/min created a very significant head drop around the sink section, greatly affecting the flow and behavior of the channel system. The calibrated final channel networks obtained from the validation and tracer test reproduction were used for this simulation. The tracer used was the same as the case of tracer test C3, HTO, and the same MPG value, settings and channel parameters were used. A particle number of was injected for the transport simulation. Thus the only thing that separated the systems was the absence of flow boundary nodes for the added injection and sink sections related to each test. The effect of this change is that the only thing driving the flow in this scenario s system is again the presence of the tunnel structure and its associated sink. The particles of the transport simulation were tracked and the exit nodes of the channels were investigated in order to map where the flow of the system exited the boundary domains of the model. In contrast to the tracer test simulations, this simulation used a resident injection mode with an instantaneous injection of the particles, not using an injection concentration curve. 26

37 3. Results The results section starts out with a short comparison between the final versions of the CNMs. The calibration result is also visualized and compared to clarify differences. After this, the different results of the tracer test reproductions are shown and compared. Lastly, the results of the leakage scenario prediction are presented. 3.1 First comparison of channel networks The final channel network of the sparse CNM consisted of 83 nodes, 74 channels and 20 fixed head boundary conditions. The final channel network of the dense CNM consisted of 6778 nodes, channels and 458 fixed head boundary conditions. The large difference in network size is fairly apparent, and its consequences will be discussed at a later stage in the discussions chapter. Figure 12 below shows the ambient flow values for the borehole/fracture intersections compared with the calibrated node throughflow values at the corresponding locations in the conceptual model. As can be seen, the sparse CNM provides a better match in most cases, with a few exceptions. 1.00E E E E E E E E E E+00 Calibration values [m 3 s -1 ] Obs. Flow Sparse CNM Dense CNM Figure 12. Comparison of calibration values obtained by the different CNMs. In figure 13 and 14 below, the final versions of the two CNMs are presented, with the hydraulic head values for the channels as well as the boreholes highlighted in green. In the sparse CNM, figure 13, the underlying fractures are visible in shaded grey. 27

38 Figure 13. Final version of the sparse CNM, boreholes in green, fractures in grey and the channel network with hydraulic head shown in color scale. Figure 14. Final version of the dense CNM, boreholes in green and the channel network with hydraulic head shown in color scale. 28

39 3.2 Comparison of tracer tests reproduction Sparse channel network model In figure 15 below, the cumulative mass recovery of the tracer tests for both CNMs are plotted versus time on a semi log graph, with the points showing the locations of 5, 50 and 95% recovery. In the cases where a 95% recovery was not obtained, the maximum recovery obtained at the end of the test is shown instead. For tracer test C1, flow path I, the Cacas sparse CNM was able to match the recovery times for 5 and 50% recovery fairly well, while the recovery for 95% of the tracer mass was less successful. A 5% recovery was reached after 8.38 hours, 50% at hours, 90% at hours and 95% at hours. In the case of tracer test C2, flow path II, the recovery times for 5 and 50% were matched to an extent, but not as well as in the case of C1. The recovery time for the 80% (maximum recovery) was much longer for the sparse method than in the case of the observed field site values. For tracer test C3, flow path III, the recovery time s match was very poor, and none of the recovery percentages were able to be matched properly. 5% recovery was reached after 7.5h, 50% recovery after 66.9 hours and 73% (maximum) recovery was reached after hours. These times are all significantly faster than the observed values, and this tracer transport simulation clearly stands out as the worst match obtained by the Cacas sparse channel model. Tracer test C4, flow path I, had the best fit for the recovery times, with all three percentage times being very closely matched. 5% was reached after 9.7 hours, 50% after 20.2 hours and 90% after hours. In table 6 below, tracer test recovery data from Andersson et al. (2002) is listed regarding tracer tests C1 to C4. The recovery times for 5, 50 and 95 percent recovery are listed, as well as the total recovery time together with the total recovery mass percentage. In addition to this, the corresponding values for the Cacas model test results are shown in table 7 below Dense channel network model The results generated by the DFN channel model were overall not as successful as the Cacas method channel network. However, it is important to note that these comparisons are between two models that performed differently after the flow calibration was complete. For tracer tests C1 and C4 with the shorter flow path I the fit was somewhat approximate but still not as precise as Cacas method. In the case of C2 and C3 the simulated transport times were significantly longer than the observed field data, and were several orders of magnitude off from being a match to the target values. The results of the tracer tests generated by the dense CNM is shown below in figure 15. For test C1, 5% mass recovery was reached after 4.73 hours, 50% recovery after 17.3 hours, 90% recovery after 131 hours and 95% recovery after hours. The fit for this tracer test is not as close as in Cacas method, but still presents a somewhat close match to the observed field values. 29

40 The DFN-generated simulation of tracer test C2 was a very poor match, and the simulated tracer transport times were significantly slower than the observed field data. 5% recovery was reached after 3.28*10 3 hours, 50% after 8.36*10 4 hours and 80% after 9.70*10 5 hours. As can be seen from figure 15 the cumulative recovery curve for C2 is skewed when comparing to the points of recovery. The same applies for tracer test C3, which also had a very poor fit for the recovery times. 5% recovery was reached after 2.31*10 3 hours, 50% after 3.770*10 4 hours and 73% after 1.81*10 5 hours. However, in the case of tracer test C4, the dense CNM showed the capability to produce a good fit for the recovery times, and the results for test C4 were a good match with the observed field test recovery times. 5% recovery was reached after 6.01 hours, 50% after hours and 90% after hours. Although this result was a marked improvement compared to the other tracer tests produced by the DFN dense method, Cacas method still obtained a closer match. In table 6, 7, and 8 the test results for the observed field values are shown, together with the corresponding simulated test results for the dense CNM. Figure 15. Results for the reproduction of tracer tests by the sparse and dense CNM. The points represent the target recovery times for the tests. 30

41 Table 6. Tracer test field site results Test Tracer t 5(h) t 50(h) t 95(h) t t (h) Recovery(%) C1 82 Br C2 ReO C3 HTO C4 131 I Table 7. Sparse CNM tracer test results Test Tracer t 5 (h) t 50 (h) t 95 (h) C1 82 Br C ReO (t 80) C3 HTO (t 73) C4 131 I (t 90) Table 8. Dense CNM tracer test results Test Tracer t 5 (h) t 50 (h) t 95 (h) C1 82 Br C ReO 4 3.3* * *10 5 (t 80) C3 HTO 2.3* * *10 5 (t 73) C4 131 I (t 90) 3.3 Canister leakage scenario prediction Figures 16 and 18 show the two respective channel networks and the exit nodes for the particles transported through the channels. As can be seen, the exit nodes of the sparse channel network are somewhat spread out in the model domain, located on several fractures, which are marked with different colors. However, the majority of the flow actually exits from fracture 7, with the flow being split between two sides of the boundary box exiting from fracture 7. This is shown in figure 16 below, with only minor outflow occurring from fractures 5, 20 and 22. Figure 17 displays a bar plot diagram which shows the representative particle exit percentage for each node and their respective fracture. Each bar column that is displayed in the bar plot represents a node in the channel network where the particles exited the boundary domain. The ID of the nodes presented in the tables represents the position of the node in the channel network, and is only used for identification purposes and serves no function besides this. In the case of the Dense CNM the particle exit nodes are more concentrated in the same area of the model boundary domain. The flow exits the system from only two fractures, 7 and 20, which occurs at the near adjacent corners of the two fractures. As in the case of the sparse CNM, it is still through fracture 7 that almost all of the flow exits the system, even more so in this case. As figure 19 depicts, the three most frequent exit nodes, all from fracture 7, carry almost all of the particles with an estimated 31

42 coverage of 98% of flow, with fracture 20 only carrying a very minimal amount of particles. Even so, the nodes on fracture 20 with the minor particle exits are still located in a very close proximity to the exit nodes on fracture 7. This entails that for the dense CNM all of the flow seems to leave the boundary domain from the same location. From this, it would appear that fracture 7 is the main exit fracture of the natural flow system, for both of the channel network models. Another conclusion from this is that the flow seems to be exiting the model boundary system through a very select amount of locations, leading to the reasoning that the flow seems to be choosing a preferential path of transport. Figure 16. Sparse CNM with particle exit nodes enlarged, particle injection node is shown in green. Percentage (%) of particle exit Sparse CNM particle tracking Particle exit node ID Fracture 7 Fracture 5 Fracture 20 Fracture 22 Figure 17. The sparse CNM particle exit nodes with their respective exit fracture 32

43 Figure 18. Dense CNM with particle exit nodes enlarged, particle injection node is shown in green Dense CNM particle tracking Percentage (%) of particle exit Particle exit node ID 266 Fracture Fracture 20 Figure 19. The dense CNM particle exit nodes with their respective exit fracture 33

44 Figure 20. Leakage scenario prediction particle recovery time As can be seen above in figure 20, the recovery time for the particle simulation was substantial for both model cases, with the sparse CNM being slightly slower. In table 9 below, the recovery times of the particle simulation for different previously used max recoveries are listed. Table 9. Recovery times of leakage scenario prediction Recovery % Sparse CNM (h) Dense CNM (h) E E E E E E E E+06 34

45 4. Discussion The discussion chapter starts out with a short discussion of the Pychan3d scripting approach. After this the recovery rate results of the tracer tests are discussed, in addition to an analysis of the causes for the differing results. The role played by the structure of flow paths is discussed, and the impact from the calibration results is analyzed. Finally, the results of the leakage scenario case is covered together with a final discussion regarding uncertainty concerning model parameters. 4.1 Pychan3d and scripting approach The study is based on a scripting approach, with the script used for generating the models being written during the work. The main segments of code used for the major steps in the method are available in the appendix. The scripting approach provided a flexible and adaptable work environment, which gave necessary space for conducting this experimental study. Since the calibration of the models were based on a manual procedure, this freedom of input was crucial in making this method feasible. The flexibility of the scripting approach is one of its greatest strengths, in that it gives the user control of how the system in question should be constructed. An example of this is the case of importing the injection curves for the tracer tests. The time of injection for the particles was found to strongly influence the end recovery time for the tracer test in question. Since all of the tracers used in this study were in essence non-sorbing, the tracer recovery curve was heavily influenced by the profile of the tracer injection curve. The ability to match the injection rate of the particles to the corresponding injection profile curve proved to be a critical part in reproducing the same conditions as for the field tracer tests. If all of the tracer concentration was injected at once, the field site results were very difficult to reproduce. On the other hand, when creating the injection curve for the Leakage Scenario Prediction case, the approach of an instantaneous injection of particles provided a more fitting scenario. Thus, the injection profile was simply set to an instantaneous injection of all the particles for the simulation. This option to manually adapt the test properties to fit specific characteristics emphasizes the strength of the adaptability of the scripting approach. In addition to this, the scripting approach was crucial in allowing for an experimental approach to be used in constructing site specific CNMs. It allowed for an investigate analysis of the model parameters, which helped increase the understanding of what parameters were more sensitive than others. As part of the aim of the study was to increase the understanding of how model parameters influence the modelling process, this constituted an important part in pursuing this aim. The same degree of experimentation with general model properties and parameters could not have been achieved by using an already established user interface. 35

46 In conclusion, using Pychan3d and a scripting approach provided the necessary tools for conducting an experimental approach to modelling the groundwater flow and transport behavior. Pychan3d was successful in constructing CNMs which respected site specific conditions. 4.2 Recovery rates In the results section the tracer test transport simulation recoveries were displayed. This showed that the recovery for 5 and 50% was obtainable for three out of the four tracer tests for the sparse CNM, and more approximately for two out of the four for the dense CNM. The final recovery was significantly more difficult to capture, and the maximum recovery was only matched in one simulation, that of tracer test C4. A potential reason for this could be the very slow recovery obtained for the higher recovery percentages. This slow recovery is especially pronounced in the very last percentages of recovery. For example, the recovery time for 90% mass recovery for the Cacas tracer test C1 was hours, while the 95% recovery was hours. The same is true for the dense CNM simulation, which showed a 90% recovery of 131 hours and a 95% recovery of 350 hours. In general, it seems that the last percentages of mass recovery were the hardest to fit, independent of how the recovery for the earlier percentages has been. In the case of the DFN-proxy model, the recovery times for test C2 and C3 were off by several orders of magnitude. This raises the question of the capability of the structure of the dense channel network, and if it is able to adequately model the flow and transport over several fractures. The current results seems to indicate that the flow is unable to find its way to the sink section in a reasonable time frame. In figure 21 below, the dense CNM flow channels for fracture 21 are shown, together with the hydraulic head levels. As can be seen, there is a large drop in hydraulic head around the sink section, which is of course expected. However, with the exception of that area there is not a large difference in hydraulic head over the channels of the fracture. As such, there is not a clear hydraulic gradient over the fracture towards the sink section, which could be one of the reasons for the extremely long transport simulation times. 36

47 Figure 21. Dense CNM fracture 21 head field, with the sink section notable in deep purple In the case of tracer test C3 and its corresponding flow path III, the observed tracer test field results were unable to be reproduced adequately. The simulated transport times from the model were significantly faster in the case of the sparse CNM, and significantly slower for the dense CNM than the observed recovery times. A potential cause for this could be the modeled structure of flow path III. According to the structural model from Hermansson and Doe, (2000) together with the field site investigations by Dershowitz et al. (2003) the flow path is characterized as a single channel flow path. While still being relatively long in length, it is still supposedly a single channel without much interference in the way of fracture and channel intersections. However, according to Andersson et al. (2002), it seems likely that flow path III is not exactly as straight forward and simple as a single channel flow path, but instead more likely to be a network flow channel, containing a more complex structure of flow paths. This fact combined with the poor reproduction of results gives cause to believe that the structure of the flow path used for the model is not an adequate representation of the actual flow path for test C3. It indeed seems likely, at least by judging from the long recovery times observed in the field, that tracer test C3 and flow path III is constituted by a flow structure more complex than in the case used for the modeling scenario. Given more time, a smaller conceptual model and respective CNM representing flow path III could have been constructed, with the intention of trying to simulate and reproduce the results of tracer test 37

48 C3. This could have been used as an attempt to try and verify if flow path III indeed could be made up by a more complex system of channels, instead of the current long single path structure in use. This potential network scale flow path hypothesis could be tested in a future project. 4.3 Flow path impact on the transport simulations The flow paths themselves most likely played a major role in determining how well the transport simulations could be matched to the original field observations. For both the sparse and the DFN based dense model the tracer tests C1 and C4, which both use flow path I, clearly showed the best results. This is possibly related to the simple nature of the flow path, not giving a large room for error. Flow path II, test C2, was reproduced in a somewhat adequate manner by the Cacas method, but it did not reach the level of precision of test C1 and C4, and in the case of the DFN model the match was far off. This also indicates that flow path II made the tracer tests more difficult to reproduce. Flow path III was thought to be simple at first, but none of the models had any success with reproducing the results for its test C3. However, as discussed above, it is possible this has other causes and explanations than the actual model structure. Since the structure of the flow paths seem to have an impact of how well the channel models can reproduce the tracer test results, the uncertainty of the conceptual model comes into question. The channel network models are based on the conceptual model constructed in this study, which in turn is based on the geological information of the structural model from Hermansson and Doe (2000) and the geological field investigations by Dershowitz et al. (2003). Since the structural model is not the true system, this brings a level of uncertainty to the flow paths. In conclusion, the longer flow paths II and III present a larger challenge for the transport simulation model, and was found to be more difficult to obtain adequate matches for. 4.4 Calibration impact Figure 12 shows the ambient flow values for the borehole/fracture intersections compared with the calibrated node throughflow values at the corresponding locations in the conceptual model. As can be seen, the sparse CNM calibrations in most cases represent a closer match to the observed field values. The dense CNM is a better fit in some cases, and is generally quite similar to the sparse version, but has a few nodes which deviate significantly from the field values. Specifically the case of the KI0023B/fracture 6 and KI0023B/fracture 20 intersections were difficult nodes to calibrate for both versions of the CNMs. As previously mentioned, these two intersections are located at the extremes of the short circuit between fractures 6 and 20, and according to Andersson et al. (1999) this short circuit is the reason for the relatively high flow values for these intersections. The fact that the sparse CNM is a closer match to the field values in this case is a good representation of how the sparse CNM was more responsive to the calibration process than the dense CNM. In order to take the short circuit into account, a direct high conductance channel was added between the KI0023B 38

49 borehole intersections of fracture 6 and 20. The exact same procedure was undertaken for both channel networks, but as shown in figure 12, with different results. The node throughflow values for the sparse CNM were one order of magnitude closer to the observed values than the dense CNM. This inability and difficulty to calibrate the dense CNM comes down to the fact that there is already a very large number of channels and nodes present in the channel network, especially when compared with the sparse CNM. During calibration when adding a channel with differing properties to the sparse CNM this often had a notable impact. As there was only a limited number of channels present for each fracture, the addition of a new channel for the fracture represented a large change in the structure of the network, and thus often resulting in a change in its parameters and values. However in the case of the dense CNM, the addition of just one channel in a fracture where there are already hundreds present, gives less of an impact. The fact remains that all the calibration done for this project was done manually, and is therefore likely more suitable to a network structure in a size such as the sparse CNM. The dense CNM could potentially perform better under an automatic calibration process, consisting of large amounts of separate changes in order to obtain the desired values for parameters. The difficulty in calibrating was a problem for the dense CNM which was not present to the same degree for the sparse CNM. Since the flow values of the dense CNM could not easily be influenced, it was more difficult to approach the target field values, which in a way makes the dense CNM less suitable for applying at site specific conditions such as this one. This comes down to an issue DFN networks in general seem to have, which is the need for very accurate field data in order to function properly. DFN networks such as the dense CNM constructed in this study is potentially a more realistic representation of the flow in fractures, but is on the other hand harder to obtain field site corresponding results from. The sparse CNM proved easier to calibrate and adjust to specific target values, but on the other hand it showed a very strong fracture dependency for its node throughflow values. For nodes located on the same fracture, it proved to be very difficult to change the value of separate nodes without influencing all of them. This had the impact of making certain calibration cases difficult to approach, especially when values of different nodes on the same fracture differed substantially. No real workaround was found for this issue, and it is a major reason to why some of the calibrated sparse CNM values are not matching the observed field data. This problem highlights a weak point of the sparse CNM; in the same way that the limited amount of channels and nodes can be an advantage during calculation, it can also become a weakness as any change made will have a large impact, potentially offsetting other calibrations previously made. As such, the system could be regarded as too sensitive to changes and adjustments. As a result of this, the model becomes difficult to calibrate in certain situations. 39

50 4.5 Leakage Scenario prediction From the results section, it would appear that fracture 7 is the main exit fracture of the natural flow system for both of the channel network models. Another conclusion from this is that the flow seems to be exiting the model boundary system through a very select amount of locations, leading to the reasoning that the flow seems to be choosing a preferential path of transport. The main difference between the two models is that in the case of the sparse CNM, the flow exits from several sides of the boundary box while for the dense CNM it exits solely from one side. Looking at the relative percentage contribution of the particle exit nodes of the two CNMs there are some apparent differences. For the sparse CNM, the flow exits from six different head boundary nodes located on the edges of the model domain boundary box. In total, there were 20 head boundary condition nodes present for the sparse CNM. This means that the six boundary condition nodes that were used by the particles as exit nodes represent 30 % of the total amount of head boundary condition nodes present in the CNM. By comparing the actual percentage of particles that exited at which node, the numbers are slightly different however % of the particles exited from fracture 7, 46.2 % from node 12 and % from node 11. Fracture 5 had the second largest amount of particles exiting, with nearly 8% through its two nodes, 5.7 % for node 3 and 2 % for node 1. In the case of the dense CNM, the flow was concentrated locally to an even greater degree. In total, there were 10 active head boundary condition nodes acting as exit nodes for particles. As the total amount of head boundary nodes amount to 458 nodes, the active exit nodes only amount to roughly 2 % of the total number of head boundary nodes. In addition to this, about 98% of the flow left the system through fracture 7, with roughly 66 % of this from just one node. This comparison shows that the flow for both CNMs occurred at around the same area, with a bit more spreading in the case of the sparse CNM. Judging from this, the flow seems to be channelized into a specific section of the fracture network, which leads to a clustering of the particle exit nodes. As a conclusion, the natural state flow of the system seems to be acting in a channelized manner, directing the flow to a very select number of fractures, independent of the CNM used. The flow of the CNMs does however leave the model boundary box through different directions, shown by the particle exit nodes present at different sides of the boundary box. Since the sparse CNM performed better in regards to calibration, it could be considered to be more trustworthy in this case. However, the dense CNM has the advantage of being able to offer more flow paths over the fractures. Since very few channels per fracture were present for the sparse CNM, the flow was very roughly directed over the fractures. As an effect of this, the final particle exit nodes for the dense CNM possibly did not even exist in the sparse CNM, as there were no channels intersecting the boundary box at that location. This showcases a potential weakness of the sparse CNM, in that its approach may be considered too simple, not accounting for potential alternative flow paths over the fractures. 40

51 This conclusion and discussion highlights a method in which CNMs generated through Pychan3d could be applied to site specific conditions in order to investigate the flow behavior of the system. The requirements being a structural or conceptual model based on verified data. The particle recovery times for both the sparse and the dense CNM were very long, and in the case of the sparse CNM the difference was substantial. An interesting detail is that the recovery time for the sparse CNM increased significantly, even reaching a recovery time longer than the dense CNM, which previously already had a quite long recovery time for test C3. A conclusion of this is that the existence of the pump section seems to have affected the sparse CNM in a much stronger way than it did for the dense CNM. This is another indicator that the sparse CNM is more sensitive to changes of the system in general, and the effects of such changes are pronounced in a strong way. 4.6 Uncertainty discussion A requirement of modelling is to reduce a real system into a simplified representation. This is especially true when modelling deep bedrock systems that are difficult to observe directly. Consequently, there is only a partial knowledge of the real system, thus resulting in large uncertainties. As many of the parameters used in the modelling processes in this study are uncertain in themselves, this brings another level of uncertainty into the model. Values of parameters such as channel width and tortuosity are at present not clearly observable by any standard technique, and must instead be estimated through means of calibration. The issue comes down to the fact that there is no real way to confirm the exact state of the deep bedrock located several hundred meters deep. Due to this, all estimates and results are subject to a large degree of uncertainty. The channel width of 0.65m used in the sparse CNM is likely on the high end as far as values for channel width in crystalline rock goes. Neretnieks et al., (2018) attempted to estimate the channel widths of crystalline bedrock at the Äspö HRL with the usage of infrared radiation waves. Certain accessible channel widths were inspected by visual inspection, and estimated to be between 5 and 10 cm. According to their estimations with infrared light on other locations, the channel widths were mostly less than 10cm. This would indicate that the value of 65 cm obtained through the calibration process as a good fit for the model is potentially not representative of the channel widths of the area. However the fact still remains that the values obtained from (Neretnieks et al., (2018) through estimation are also subject to uncertainty. In their report, it is mentioned that the uncertainty for the method of estimation of the channel widths is on the order of a factor between 2 and 5. As such, the value of 65cm is on the outer range, but not unjustifiably far away from the range of uncertainty regarding the channel width. One should also note that the value of 0.65m was obtained through calibration using a CNM based on a set fracture network structure. It is possible that the relatively high estimated value of width could simply be related to the scripting library used, Pychan3d, as all of the calibrations and results are subject to the underlying rules of 41

52 Pychan3d. However, the fact that the value 0.65m was obtained as adequate for reproducing the majority of the tracer tests might as well be related to the general structure of the fracture network the modelling procedure is located in. This further highlights the fact that the parameters used for channel networks are prone to be affected by many factors, and a wide range of values for the parameters could be applied. Furthermore, the channel width was found to be one of the more sensitive parameters during the calibration session, as minor changes such as changing from 0.65 to 0.6 meters width could mean the difference between the model properly reproducing transport simulations for the tracer tests, and not being able to. In a way, all parameters were very sensitive, but as the main ones manually calibrated were tortuosity and width, these two were the ones experimented with the most, and thus gained the most insight into. The fact that the channel aperture parameter was calculated through the cubic law entails that the result could be considered somewhat biased. Fracture surface roughness and aperture variation has a large impact on flow behavior, and the fact that this is not taken into account by the cubic law has led to most attempts using measured aperture values being less successful at calculating the flow rates (Konzuk and Kueper, 2004). One idea to approach this problem is to account for the aperture variations by using a local cubic law method, with more localized values for aperture. For the sparse CNM, the aperture is calculated by the cubic law for every channel, which gives a relatively local aperture value, partially mitigating the problems associated with applying a mean aperture value for all flow calculations. However, the aperture calculated by the cubic law assumes that the aperture of the channel is constant and the same as the opening of the channel, which likely is not the case. So the end result ends up being a local channel aperture value which is still a bit skewed and biased, as the potential variations of the aperture cannot be taken into consideration for the entire channel. For the dense DFN, which uses a fracture wide aperture value, the same problem definitely applies as well. The values are less localized than in the sparse CNM, with one aperture value applying to hundreds of flow channels for each fracture. This broad generalization of the aperture could potentially be one reason for the difficulties had in calibrating the dense CNM. The tortuosity was the other parameter, other than the width, that was completely decided through estimation by calibration, and as such was subject to the uncertainty this entails. The tortuosity in itself was not as sensitive as the width parameter, from a relative point of view. Changing the value of the tortuosity parameter still had a clearly noticeable impact on the transport of flow, but larger changes had to be made in order to obtain the same change in the modelled outcome. The reasons for this smaller impact from tortuosity may be difficult to explain directly, but could be related to the aperture values. Tsang (1984) links the effect of tortuosity on fluid flow to the size of the aperture values, with smaller aperture values causing the tortuosity to have a greater impact. The calculated aperture values for the CNMs used for this study is around the magnitude of 10-4 meters, which could be considered quite small. This then raises the question why changes in the 42

53 tortuosity is not more sensitive than the width parameter. The case could however be that actual impact of the tortuosity is already relatively significant, and would have been even smaller in the case of larger aperture values. The conclusion from this is that it is most likely not possible to determine from the results of this study if the current impact of tortuosity is reasonable or not. In addition to the uncertainty associated with the parameters used, the fact that the transport model used by the CNMs in the study does not take dispersion into account is another source of uncertainty. Dispersion is most likely an important process in a fractured and heterogeneous system such as the one studied and modelled in this thesis. The lack of dispersion can thus be considered a weak point of this modelling study, and this needs to be taken into account when analyzing the results generated. An interesting continuation of the modelling work with Pychan3d could be to develop a way to include dispersion, and approach the same study area with the addition of this. This could be used to compare the success rate of the models with and without the influence of dispersion on the transport. 4.7 Future work This subchapter shortly lists potential future projects based on this study that could be undertaken. The flow path of tracer test C3, flow path II, proved to be very difficult to reproduce. As mentioned this could be due to the fact that the actual structure of the flow path is more complicated than the structure first obtained from the model by Hermansson and Doe (2000). This study did not have the time to further investigate the causes for this. Given more time, a CNM focusing on flow path II assuming a multiple channel approach could have been developed. This smaller CNM could be used to investigate if more reasonable transport times could be obtained with this approach. The results obtained from this could indicate if a multiple channel approach would be more representative of the flow path structure or not. The effect of dispersion is another factor which would be interesting to include in a future study, as this constitutes a major influence on how groundwater transport behaves. As of now, the inclusion of dispersion was not supported by Pychan3d, but given time the effect of dispersion could be included into the scripting library and consequently be included into models created by it. A future study could be made with the inclusion of dispersion, and be used to further the understanding on how to apply CNMs to site specific conditions. In addition to the above mentioned, an option of developing a third alternative CNM would be a beneficial addition to this work. The current sparse and dense CNMs both act as an extreme in its approach, with either very few channels or a very large amount of channels per fracture. An interesting approach would thus be to develop a third alternative to these two, which could meet somewhere in the middle between the sparse and the dense approach. This would offer a view point and alternative which is not as extreme in its distribution of channels, and could potentially provide a more adequate representation of the field site. This approach could help increase the understanding of what parameters 43

54 from the alternative CNMs carry the most weight, and in which direction the future development of CNMs should go. 44

55 5. Conclusions The Pychan3d scripting library was successfully used to create channel network models respecting specific conditions from the TRUE-Block Scale site. The scripting approach provided a flexible workflow which allowed for adaptations to the specific conditions of the field site. This approach was crucial in enabling the testing of different model characteristics and properties. The sparse CNM was found to give very adequate flow and transport responses in most cases, while the dense CNM was unable to generate results of the same standard. The leakage scenario prediction established that the long term natural state flow seems to be following a highly channelized flow pattern, concentrating the main part of the flow to a few select fractures, with some variations between the two CNMs. The sparse CNM was found to be more responsive to calibration, as well as being more sensitive to changes in general. Possibly as an effect of this, the sparse CNM was more successfully applied to a field specific site when compared to the DFN-proxy dense CNM. The sparse CNM did have a closer match to the flow values after calibration, and as such, could be expected to perform better. The issue of calibration regarding the dense CNM is possibly related to key parameters being defined uniformly in each embedding fracture, but is also likely an effect of the large size of the model and the difficulty in manually calibrating it. All of the parameters used for the modelling process can be considered to have a large impact. However, the channel width was found to be the most sensitive during calibration, with minor changes causing a large impact on the transport simulations of the CNMs. More insight is needed about the impact of channel tortuosity. In addition, the calculated aperture values are subject to some degree of bias and uncertainty, due to the nature of the cubic law and its inability to account for variations in the fracture and channel apertures. 45

56 6. Acknowledgements First and foremost, I would like to thank my supervisor, Benoît Dessirier, for all the hours put in giving me invaluable help and advice during the process of the thesis. The support given by him exceeded all expectations I had of him as a supervisor, and I am so grateful for his support during this thesis. I would also like to thank my fellow master students who have made the years here at Uppsala University a truly amazing experience. Thank you Maria, Matilda, Sigrún, Friða, Patrick, Einar, Emil, Aryani and Yang and Kate for the time spent here together. An extra thank you goes out to Matilda, who provided much needed help with the creation and modification of figures for both the thesis and presentation. 46

57 7. Reference list Andersson, P., Byegård, J., Holmqvist, M., Skålberg, M., Wass, E., Widestrand, H., Äspö Hard Rock Laboratory True Block Scale Project Tracer test stage Tracer tests, Phase C (No. IPR-01-33). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. Andersson, P., Dershowitz, B., Hermansson, J., Meier, P., Tullborg, E.-L., Winberg, A., Final report of the TRUE Block Scale Project, 1. Characterisation and model development. (No. TR-02-13). Stockholm. Available at: [ ]. Andersson, P., Jan-Erik Ludvigsson, Eva Wass, Magnus Holmqvist, Äspö Hard Rock Laboratory TRUE Block Scale Project Tracer test stage Interference tests, dilution tests and tracer tests. (No. IPR-00-28). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. Andersson, P., Jan-Erik Ludvigsson, Eva Wass, Magnus Holmqvist, Äspö Hard Rock Laboratory TRUE Block Scale Detailed characterisation stage Interference tests and tracer tests PT-1 PT-4 (No. IPR-01-52). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. Berkowitz, B., Characterizing flow and transport in fractured geological media: A review. Advances in Water Resources 25, Berkowitz, B., Naumann, C., Smith, L., Mass transfer at fracture intersections: An evaluation of mixing models. Water Resources Research 30, Cacas, M.C., Ledoux, E., De Marsily, G., Tillie, B., Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model. Water Resources Research 26, Dagan, G., Solute plumes mean velocity in aquifer transport: Impact of injection and detection modes. Advances in Water Resources, Tribute to Professor Garrison Sposito: An Exceptional Hydrologist and Geochemist 106, Dershowitz, W., Anders Winberg, Jan Hermansson, Johan Byegård, Eva-Lena Tullborg, Peter Andersson, Martin Mazurek, Äspö Task Force on modelling of groundwater flow and transport of solutes Task 6c A semi-synthetic model of block scale conductive structures at the Äspö HRL (No. IPR-03-13). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. Dessirier, B., Tsang, C.-F., Niemi, A., A new scripting library for modeling flow and transport in fractured rock with channel networks. Computers & Geosciences 111, Figueiredo, B., Tsang, C.-F., Niemi, A., Lindgren, G., Review: The state-of-art of sparse channel models and their applicability to performance assessment of radioactive waste repositories in fractured crystalline formations. Hydrogeol J 24, x Frampton, A., Cvetkovic, V., Significance of injection modes and heterogeneity on spatial and temporal dispersion of advecting particles in two-dimensional discrete fracture networks. Advances in Water Resources, Dispersion in Porous Media 32, Geuzaine, C., Remacle, J.-F., Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 79,

58 Hartley, L., Jackson, P., Joyce, S., Roberts, D., Shevelan, J., Swift, B., Gylling, B., Marsic, N., Hermansson, J., Öhman, J., Hydrogeological pre-modelling exercises (No. R-07-57). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. Hermansson, J., Doe, T., Äspö Hard Rock Laboratory March 00 structural and hydraulic model based on borehole data from Kl0025F03 (No. IPR-00-34). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. Hyman, J.D., Karra, S., Makedonska, N., Gable, C.W., Painter, S.L., Viswanathan, H.S., dfnworks: A discrete fracture network framework for modeling subsurface flow and transport. Computers & Geosciences 84, Kang, P.K., Dentz, M., Le Borgne, T., Lee, S., Juanes, R., Anomalous transport in disordered fracture networks: Spatial Markov model for dispersion with variable injection modes. Advances in Water Resources, Tribute to Professor Garrison Sposito: An Exceptional Hydrologist and Geochemist 106, Kluyver, T., Ragan-Kelley, B., Pérez, F., Ganger, G., Bussonnier, M., Frederic, J., Kelley, K., Hamrick, J., Grout, J., Corlay, S., Ivanov, P., Avila, D., Abdalla, S., Willing, C., Jupyter Notebooks a publishing format for reproducible computational workflows. Available at: [ ] Konzuk, J.S., Kueper, B.H., Evaluation of cubic law based models describing single phase flow through a rough walled fracture. Water Resources Research Kornfält, K.-A., Persson, P.-O., Wikman, H., Granitoids from the Äspö area, southeastern Sweden geochemical and geochronological data. GFF 119, Lei, Q., Latham, J.-P., Tsang, C.-F., The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks. Computers and Geotechnics 85, Li, S.C., Xu, Z.H., Ma, G.W., A Graph-theoretic Pipe Network Method for water flow simulation in discrete fracture networks: GPNM. Tunnelling and Underground Space Technology 42, Long, J.C.S., Remer, J.S., Wilson, C.R., Witherspoon, P.A., Porous media equivalents for networks of discontinuous fractures. Water Resources Research 18, Mahmoudzadeh, B., Liu, L., Moreno, L., Neretnieks, I., Solute transport in fractured rocks with stagnant water zone and rock matrix composed of different geological layers-model development and simulations: MODELING SOLUTE TRANSPORT IN FRACTURED ROCKS. Water Resources Research 49, Moreno, L., Crawford, J., Can we use tracer tests to obtain data for performance assessment of repositories for nuclear waste? Hydrogeol J 17, Moreno, L., Neretnieks, I., Fluid flow and solute transport in a network of channels. Journal of Contaminant Hydrology 14, Neretnieks, I., Moreno, L., Liu, L., Mahmoudzadeh, B., Shahkarami, P., Maskenskaya, O., Kinnbom, P., Use of infrared pictures to assess flowing channel frequencies and flowrates in fractured rocks (No. R-17-04). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. 48

59 Nordqvist, R., Johan Byegård, Calle Hjerne, Feasibility study of a Single Well Injection Withdrawal (SWIW) experiment with synthetic groundwater (No. R ). Svensk Kärnbränsehantering AB, Stockholm. Available at: [ ]. Oliphant, T., E., Guide to Numpy. Trelgol Publishing USA. Available at: [ ]. Oliphant, T.E., Python for Scientific Computing. Computing in Science Engineering 9, Stanfors, R., Rhén, I., Tullborg, E.-L., Wikberg, P., Overview of geological and hydrogeological conditions of the Äspö hard rock laboratory site. Applied Geochemistry 14, Tsang, C.-F., Neretnieks, I., Flow channeling in heterogeneous fractured rocks. Reviews of Geophysics 36, Tsang, C.-F., Neretnieks, I., Tsang, Y., Hydrologic issues associated with nuclear waste repositories. Water Resources Research 51, Tsang, Y.W., The Effect of Tortuosity on Fluid Flow Through a Single Fracture. Water Resources Research 20, Witherspoon, P.A., Wang, J.S.Y., Iwai, K., Gale, J.E., Validity of Cubic Law for fluid flow in a deformable rock fracture. Water Resources Research 16, Wu, T., Wang, H., Zheng, Q., Zhao, Y.L., Van Loon, L.R., Diffusion behavior of Se(IV) and Re(VII) in GMZ bentonite. Applied Clay Science 101, Yuan-Hui, L., Gregory, S., Diffusion of ions in sea water and in deep-sea sediments. Geochimica et Cosmochimica Acta 38,

60 8. Appendix 8.1 Appendix Python code Presented below is the code written in python for generating the models used in the study. The script covers all of the main parts presented in the method Defining and creating a DFN #importing fracture data import numpy as np from pychan3d import DiscreteFractureNetwork, Node, Channel table_corner1 = np.loadtxt('new_features.csv', skiprows = 2, usecols = (8,9,10), delimiter = ';') table_corner2 = np.loadtxt('new_features.csv', skiprows = 2, usecols = (11,12,13), delimiter = ';') table_corner3 = np.loadtxt('new_features.csv', skiprows = 2, usecols = (14,15,16), delimiter = ';') table_corner4 = np.loadtxt('new_features.csv', skiprows = 2, usecols = (17,18,19), delimiter = ';') table_id = np.loadtxt('new_features.csv', skiprows = 2, usecols = (0,), delimiter = ';', dtype = str) trans_values = np.loadtxt('new_features.csv', skiprows = 2, usecols = (3), delimiter = ';') #Creating fracture nodes nfrac = 10 mynode = [] for k in range(0, len(table_corner1)): lastnode = [] lastnode.append(node((table_corner1[k, 0]), (table_corner1[k, 1]), (table_corner1[k, 2]))) lastnode.append(node((table_corner2[k, 0]), (table_corner2[k, 1]), (table_corner2[k, 2]))) lastnode.append(node((table_corner3[k, 0]), (table_corner3[k, 1]), (table_corner3[k, 2]))) lastnode.append(node((table_corner4[k, 0]), (table_corner4[k, 1]), (table_corner4[k, 2]))) mynode.extend(lastnode) #Create fracture boundary sequence myfract = [[i * 4, i * 4 + 1, i * 4 + 2, i * 4 + 3] for i in range(nfrac)] xmin, xmax = 1820., ymin, ymax = 7070., zmin, zmax = -550., mynode.append(node(xmin, ymin, zmin)) mynode.append(node(xmax, ymin, zmin)) mynode.append(node(xmax, ymax, zmin)) mynode.append(node(xmin, ymax, zmin)) mynode.append(node(xmin, ymin, zmax)) mynode.append(node(xmax, ymin, zmax)) mynode.append(node(xmax, ymax, zmax)) mynode.append(node(xmin, ymax, zmax)) l = len(mynode) 50

61 mybnd = [[l-8, l-7, l-6, l-5],[l-4, l-3, l-2, l-1], [l-8, l-7, l-3, l-4],[l-5, l-6, l-2, l-1], [l-7, l-6, l-2, l-3],[l-8, l-5, l-1, l-4]] #borehole info borehole_table = np.loadtxt('point_coords.csv', delimiter=';', usecols=(1,2,3,4,5,6), skiprows=1) borehole_names = np.loadtxt('point_coords.csv', delimiter=';', usecols=(0), skiprows=1, dtype=str) myboreholes = [] for bh in range(borehole_table.shape[0]): myboreholes.append([len(mynode), len(mynode)+1]) mynode.append(node(borehole_table[bh, 0], borehole_table[bh, 1], borehole_table[bh, 2])) mynode.append(node(borehole_table[bh, 3], borehole_table[bh, 4], borehole_table[bh, 5])) #network creation #help(discretefracturenetwork) mydfn = DiscreteFractureNetwork(nodes=myNode, fractures=myfract, fracture_names = table_id[:nfrac], boundaries=mybnd, boreholes=myboreholes, borehole_names=borehole_names) mydfn.calculate_boundary_intersections() mydfn.calculate_intersections() mydfn.calculate_borehole_intersections() mydfn.check_multiple_intersections(tol=1.e-3) print(mydfn) mydfn.export2vtk('pure_dfn') mydfn.save_to_file('pure_dfn') Sparse CNM creation import numpy as np from pychan3d import DiscreteFractureNetwork, Node, Channel mydfn = DiscreteFractureNetwork() mydfn.load_from_file('pure_dfn') print(mydfn) #export to channel network mycnm, bndnodes, bh_nodes = mydfn.create_channel_network(scheme='cacas', fparams={'transmissivity': [trans_values[i] for i in range(len(myfract))]}, w = 0.65, skip_fractures=(mydfn.fracture_name2index['23'],)) mycnm.export2vtk('cnm_cacas') print(bh_nodes[('ki0023b', '20')]) print(mycnm.nodes[bh_nodes[('ki0023b', '20')]]) print(mydfn.fracture_name2index) print(mydfn.borehole_name2index) print(mydfn.borehole_intersections) #print(mycnm.node_throughflows[bh_nodes[('ki0025f', '22')]]) print(mycnm) Dense CNM creation 51

62 import numpy as np from pychan3d import DiscreteFractureNetwork, Node, Channel mydfn = DiscreteFractureNetwork() mydfn.load_from_file('pure_dfn') print(mydfn) #export to channel network mycnm, bndnodes, bh_nodes = mydfn.create_channel_network(scheme='dfn', fparams={'transmissivity': [trans_values[i] for i in range(len(myfract))]}, w = 0.65, skip_fractures=(mydfn.fracture_name2index['23'],)) mycnm.export2vtk('cnm_cacas') print(bh_nodes[('ki0023b', '20')]) print(mycnm.nodes[bh_nodes[('ki0023b', '20')]]) print(mydfn.fracture_name2index) print(mydfn.borehole_name2index) print(mydfn.borehole_intersections) #print(mycnm.node_throughflows[bh_nodes[('ki0025f', '22')]]) print(mycnm) Sparse CNM calibration and adding of channels from pychan3d import Node, Channel, Network, BND_COND, TransportSimulation, DiscreteFractureNetwork, load_network import pickle import numpy as np from copy import copy mydfn = DiscreteFractureNetwork() mydfn.load_from_file('true-block-scale_dfn') # to load: mycnm = load_network('true-block-scale_cnm_cacas') with open('true-block-scale_cnm_cacas_bndnodes', 'rb') as f: bndnodes = pickle.load(f) with open('true-block-scale_cnm_cacas_bh_nodes', 'rb') as f: bh_nodes = pickle.load(f) print(mycnm) #Adding channels from pychan3d import Channel #nod = Node(1828, 7275, -480) #nod_a = Node(1870, 7180, -550) rep_chan_1 = mycnm.channels[24,40] rep_chan_2 = mycnm.channels[26, 40] rep_chan_3 = mycnm.channels[19, 41] rep_chan_4 = mycnm.channels[33, 44] rep_chan_5 = mycnm.channels[29, 43] rep_chan_6 = mycnm.channels[8, 41] rep_chan_7 = mycnm.channels[29, 41] rep_chan_8 = mycnm.channels[32, 41] rep_chan_9 = mycnm.channels[33, 43] rep_chan_10 = mycnm.channels[5, 36] rep_chan_11 = mycnm.channels[29, 41] chan = Channel(conductance = 5.5e-10, width=5.00e-1) chan_two = Channel(conductance = 2.77e-8, width = 5.00e-1) chan_three = Channel(conductance = 3.5e-5, width = 5.00e-1,) ch_bh_one = Channel(conductance = 2.77e-7, width = 5.00e-1) 52

63 ch_bh_two = Channel(conductance = 1.38e-7, width = 5.00e-1) ch_bh_thr = Channel(conductance = 8.33e-8, width = 5.00e-1) ch_bh_fo = Channel(conductance =2.77e-5, width = 5.00e-1) ch_bh_fi = Channel(conductance = 5.55e-8, width = 5.00e-1) ch_bh_six = Channel(conductance = 1.11e-7, width = 5.00e-1) ch_bh_sev = Channel(conductance = 2.77e-9, width = 5.00e-1) ch_bh_eig = Channel(conductance = 3.88e-8, width = 5.00e-1) ch_bh_nin = Channel(conductance = 8.33e-9, width = 5.00e-1) ch_bh_ten = Channel(conductance = 2.77e-8, width = 5.00e-1) mycnm.add_channel(36, (bh_nodes['ki0023b', 'fract_6']), ch_bh_fo) mycnm.add_channel((bh_nodes['ki0023b', 'fract_6']), (bh_nodes['ki0025f02', 'fract_6']), ch_bh_thr) mycnm.add_channel(5, (bh_nodes['ki0025f02', 'fract_6']), copy(rep_chan_10)) mycnm.add_channel(39, (bh_nodes['ki0023b', 'fract_13']), ch_bh_fi) mycnm.add_channel((bh_nodes['ki0025f02', 'fract_13']), (bh_nodes['ki0023b', 'fract_13']), ch_bh_six) mycnm.add_channel(21, (bh_nodes['ki0025f02', 'fract_13']), copy(mycnm.channels[21, 39])) mycnm.add_channel(39, (bh_nodes['ka2563a', 'fract_13']), ch_bh_sev) mycnm.add_channel(7, (bh_nodes['ka2563a', 'fract_13']), copy(mycnm.channels[7, 39])) mycnm.remove_channel(7, 39) mycnm.add_channel(40, (bh_nodes['ka2563a', 'fract_19']), ch_bh_one) mycnm.add_channel(24, (bh_nodes['ka2563a', 'fract_19']), rep_chan_1) mycnm.remove_channel(24, 40) mycnm.add_channel(40, (bh_nodes['ki0023b', 'fract_19']), ch_bh_eig) mycnm.add_channel(26, (bh_nodes['ki0023b', 'fract_19']), rep_chan_2) mycnm.remove_channel(26,40) mycnm.add_channel((bh_nodes[('ka2563a', 'fract_20')]), 41, copy(ch_bh_one)) mycnm.add_channel((bh_nodes[('ka2563a', 'fract_20')]), 8, rep_chan_6) mycnm.remove_channel(8, 41) mycnm.add_channel((bh_nodes[('ki0025f02', 'fract_20')]), 41, ch_bh_two) mycnm.add_channel((bh_nodes[('ki0025f02', 'fract_20')]), 29, rep_chan_7) #mycnm.remove_channel(29,41) removed later mycnm.add_channel(41,(bh_nodes[('ki0025f', 'fract_20')]), copy(ch_bh_sev)) mycnm.add_channel(32, (bh_nodes[('ki0025f', 'fract_20')]), copy(rep_chan_8)) mycnm.remove_channel(32, 41) mycnm.add_channel(41, (bh_nodes[('ki0023b', 'fract_20')]), copy(ch_bh_fo)) mycnm.add_channel(19, (bh_nodes[('ki0023b', 'fract_20')]), rep_chan_3) mycnm.remove_channel(19, 41) mycnm.add_channel(42, (bh_nodes[('ki0023b', 'fract_21')]), ch_bh_nin) mycnm.add_channel((bh_nodes[('ki0023b', 'fract_21')]), (bh_nodes[('ki0025f02', 'fract_21')]), copy(ch_bh_six)) mycnm.add_channel(20, (bh_nodes[('ki0025f02', 'fract_21')]), copy(ch_bh_six)) mycnm.add_channel(43, (bh_nodes[('ki0025f02', 'fract_22')]), copy(ch_bh_one)) mycnm.add_channel(33, (bh_nodes[('ki0025f02', 'fract_22')]), rep_chan_9) mycnm.remove_channel(33,43) mycnm.add_channel(44, (bh_nodes[('ki0025f02','fract_23')]), ch_bh_ten) mycnm.add_channel(33, (bh_nodes[('ki0025f02','fract_23')]), rep_chan_4) mycnm.remove_channel(33, 44) mycnm.add_channel(29,43, copy(rep_chan_5)) mycnm.add_channel(21,29, copy(rep_chan_5)) mycnm.add_channel(21,34, copy(rep_chan_5)) mycnm.remove_channel(29,43) mycnm.remove_channel(21,43) mycnm.remove_channel(34,43) 53

64 #Tracer test boreholes mycnm.add_channel(41, (bh_nodes[('ki0025f03', 'fract_20')]), copy(rep_chan_11)) mycnm.add_channel(29, (bh_nodes[('ki0025f03', 'fract_20')]), copy(rep_chan_11)) mycnm.remove_channel(29, 41) mycnm.add_channel((bh_nodes[('ki0025f02', 'fract_23')]), (bh_nodes[('ki0025f03', 'fract_23')]), copy(ch_bh_ten)) mycnm.add_channel((bh_nodes[('ki0023b', 'fract_6')]), (bh_nodes[('ki0023b', 'fract_20')]), chan_three) #Fixing the no flow of fracture 23 #mycnm.add_channel(36, 44, copy(chan_two)) mycnm.add_channel(13, 44, copy(chan_three)) print('done') #mycnm.add_channel(75, (len(mycnm.nodes)-1), chan_two) #mycnm.export2vtk('test_channel') #Calibrating channels for k, v in mycnm.channels.items(): if 68 in k: mycnm.channels[k].conductance *= 100 print(v) for k, v in mycnm.channels.items(): if 78 in k: mycnm.channels[k].conductance *= 100 print(v) for k, v in mycnm.channels.items(): if 60 in k: mycnm.channels[k].conductance *= 100 print(v) print(mycnm) for k, v in mycnm.channels.items(): if 63 in k: mycnm.channels[k].conductance /= 100 print(v) Dense CNM calibration and adding of channels from pychan3d import Node, Channel, Network, BND_COND, TransportSimulation, DiscreteFractureNetwork, load_network import pickle import numpy as np from copy import copy mydfn = DiscreteFractureNetwork() mydfn.load_from_file('true-block-scale_dfn') # to load: mycnm = load_network('true-block-scale_cnm_dfn-like') with open('true-block-scale_cnm_dfn-like_bndnodes', 'rb') as f: bndnodes = pickle.load(f) with open('true-block-scale_cnm_dfn-like_bh_nodes', 'rb') as f: bh_nodes = pickle.load(f) print(mycnm) chan_three = Channel(conductance = 3.5e-5, width = 5.00e-1) mycnm.add_channel((bh_nodes[('ki0023b', 'fract_6')]), (bh_nodes[('ki0023b', 'fract_20')]), chan_three) for chan in mycnm.channels.values(): chan.conductance *= Interpolation of head values 54

65 import numpy as np from pychan3d import Node, Channel, Network, BND_COND, TransportSimulation, DiscreteFractureNetwork, load_network #interpolation of head values bndnodes = list(bndnodes) boundary_nodes = [] #mycnm.nodes[bndnodes] for item in range(len(bndnodes)): boundary_nodes.append(mycnm.nodes[bndnodes[item]]) len(bndnodes) B_N = np.array(boundary_nodes) xhead = np.loadtxt('heads.csv', skiprows = 2, usecols = (0), delimiter = ';') yhead = np.loadtxt('heads.csv', skiprows = 2, usecols = (1), delimiter = ';') zhead = np.loadtxt('heads.csv', skiprows = 2, usecols = (2), delimiter = ';') head_values = np.loadtxt('heads.csv', skiprows = 2, usecols = (3), delimiter = ';') head_coords = np.loadtxt('heads.csv', skiprows = 2, usecols = (0, 1, 2, 3), delimiter = ';') from scipy.interpolate import griddata for item in range(0, len(b_n)): ip = griddata((xhead,yhead,zhead), head_values, (mycnm.nodes[bndnodes[item]]), method='nearest') mycnm.add_hboundary(bndnodes[item], ip) print(mycnm) dic = mycnm.clean_network(return_dic=true) bh_nodes = {k: dic[v] for k, v in bh_nodes.items() if v in dic} mycnm.set_channel_lengths(length=none, tort=2.2) #mycnm.set_channel_widths(width=0.65) Sparse CNM transport simulation tracer tests from pychan3d import Node, Channel, Network, BND_COND, TransportSimulation, DiscreteFractureNetwork, load_network import pickle import numpy as np from copy import copy dic = mycnm.clean_network(return_dic=true) bh_nodes = {k: dic[v] for k, v in bh_nodes.items() if v in dic} mycnm.set_channel_lengths(length=none, tort=2.2) mycnm.set_channel_widths(width=0.65) mycnm.solve_steady_state_flow_scipy_direct() mycnm.export2vtk('flow_paths') #Tracer test C1 Br-82 mycnm.set_channel_apertures() #Sink 55

66 mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f03', 'fract_20')], e-7) #mycnm.clean_network() mycnm.solve_steady_state_flow_scipy_direct() #Br-82 t = [0, 0.35*3600, 1*3600, 4*3600, 10*3600, 20*3600, 40*3600, 100*3600, 150*3600, 180*3600] c = [0, 2.5e-3, 1.5e-1, 5e-2, 1.5e-2, 2.5e-3, 9e-4, 5e-4, 5e-4, 0] #Na-24 #t= [0, 0.3*3600, 1*3600, 4*3600, 10*3600, 20*3600, 30*3600, 35*3600] #c= [0, 1e-3, 1.4e-1, 5.5e-2, 1.5e-2, 2.5e-3, 4e-4, 0] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f03', 'fract_20')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=30000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() mycnm.export2vtk('cnm_cacas_flow_cone') TS.set_channel_matrix_models(channels='all', R=1., MPG=5e-7) print(recovery) TS.run_particle_tracking() #Tracer test C2 ReO4- #Changing width, tort and aperture #mycnm.set_channel_lengths(length=none, tort=2.) #mycnm.set_channel_widths(width=0.7) mycnm.set_channel_apertures() #Sink mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f03', 'fract_23')], e-7) #mycnm.clean_network() mycnm.solve_steady_state_flow_scipy_direct() t= [0, 0.4*3600, 1*3600, 10*3600, 20*3600, 50*3600, 100*3600, 180*3600, 200*3600] c= [0, 5e-3, 2e-1, 8e-2, 2.5e-2, 4e-3, 5.5e-4, 4e-4, 0] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f03', 'fract_23')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=30000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() mycnm.export2vtk('cnm_cacas_flow_ctwo') TS.set_channel_matrix_models(channels='all', R=1., MPG=6.62e-7) print(recovery) TS.run_particle_tracking() #Tracer test C3 HTO #Changing width, tort and aperture #mycnm.set_channel_lengths(length=none, tort=2.) #mycnm.set_channel_widths(width=0.7) 56

67 mycnm.set_channel_apertures() #sink mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325.e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f02', 'fract_21')], 3.e-8) mycnm.solve_steady_state_flow_scipy_direct() c = [0, 2e-2, 7e-2, 1e-1, 2e-2, 2e-4, 9e-6, 0] t = [0, 0.5*3600, 1*3600, 10*3600, 100*3600, 450*3600, 900*3600, 1000*3600] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f02', 'fract_21')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=30000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() TS.set_channel_matrix_models(channels='all', R=1., MPG=3.94e-6) #mycnm.export2vtk('cnm_cacas_flow_cthree') print(recovery) TS.run_particle_tracking() #Tracer test C4 I-131 #Changing width, tort and aperture #mycnm.set_channel_lengths(length=none, tort=2.) #mycnm.set_channel_widths(width=0.7) mycnm.set_channel_apertures() #mycnm.set_channel_apertures(aperture=1.e-3) #sink mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f03', 'fract_20')], e-7) #mycnm.clean_network() mycnm.solve_steady_state_flow_scipy_direct() c= [0, 3e-4, 2e-2, 5e-2, 1e-2, 1.5e-3, 4e-4, 3e-4, 0] t= [0, 0.3*3600, 0.6*3600, 2*3600, 10*3600, 20*3600, 25*3600, 30*3600, 35*3600] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f03', 'fract_20')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=30000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() mycnm.export2vtk('cnm_cacas_flow_cfour') TS.set_channel_matrix_models(channels='all', R=1., MPG= e-07) print(recovery) TS.run_particle_tracking() Dense CNM transport simulation tracer tests from pychan3d import Node, Channel, Network, BND_COND, TransportSimulation, DiscreteFractureNetwork, load_network import pickle import numpy as np 57

68 from copy import copy mycnm.solve_steady_state_flow_scipy_direct() mycnm.export2vtk('dfn_network_final_flow') #Tracer test C1 Br-82 #mycnm.set_channel_apertures() #Sink mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f03', 'fract_20')], e-7) #mycnm.clean_network() mycnm.solve_steady_state_flow_scipy_direct() #Br-82 t = [0, 0.35*3600, 1*3600, 4*3600, 10*3600, 20*3600, 40*3600, 100*3600, 150*3600, 180*3600] c = [0, 2.5e-3, 1.5e-1, 5e-2, 1.5e-2, 2.5e-3, 9e-4, 5e-4, 5e-4, 0] #Na-24 #t= [0, 0.3*3600, 1*3600, 4*3600, 10*3600, 20*3600, 30*3600, 35*3600] #c= [0, 1e-3, 1.4e-1, 5.5e-2, 1.5e-2, 2.5e-3, 4e-4, 0] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f03', 'fract_20')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=1000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() mycnm.export2vtk('cnm_dfn_flow_cone') TS.set_channel_matrix_models(channels='all', R=1., MPG=5e-7) print(recovery) TS.run_particle_tracking() #Tracer test C2 ReO4- #Changing width, tort and aperture #mycnm.set_channel_lengths(length=none, tort=2.) mycnm.set_channel_apertures() #Sink mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f03', 'fract_23')], e-7) #mycnm.clean_network() mycnm.solve_steady_state_flow_scipy_direct() t= [0, 0.4*3600, 1*3600, 10*3600, 20*3600, 50*3600, 100*3600, 180*3600, 200*3600] c= [0, 5e-3, 2e-1, 8e-2, 2.5e-2, 4e-3, 5.5e-4, 4e-4, 0] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f03', 'fract_23')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=30000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() 58

69 mycnm.export2vtk('cnm_dfn_flow_ctwo') TS.set_channel_matrix_models(channels='all', R=1., MPG=6.62e-7) print(recovery) TS.run_particle_tracking() #Tracer test C3 HTO #Changing width, tort and aperture #mycnm.set_channel_lengths(length=none, tort=2.) #mycnm.set_channel_widths(width=0.7) mycnm.set_channel_apertures() #sink mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325.e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f02', 'fract_21')], 3.e-8) mycnm.solve_steady_state_flow_scipy_direct() c = [0, 2e-2, 7e-2, 1e-1, 2e-2, 2e-4, 9e-6, 0] t = [0, 0.5*3600, 1*3600, 10*3600, 100*3600, 450*3600, 900*3600, 1000*3600] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f02', 'fract_21')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=30000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() TS.set_channel_matrix_models(channels='all', R=1., MPG=3.94e-6) #mycnm.export2vtk('cnm_cacas_flow_cthree') print(recovery) TS.run_particle_tracking() #Tracer test C4 I-131 #Changing width, tort and aperture #mycnm.set_channel_lengths(length=none, tort=2.) #mycnm.set_channel_widths(width=0.7) mycnm.set_channel_apertures() #sink mycnm.add_qboundary(bh_nodes[('ki0023b', 'fract_21')], -325e-7) #injection mycnm.add_qboundary(bh_nodes[('ki0025f03', 'fract_20')], e-7) #mycnm.clean_network() mycnm.solve_steady_state_flow_scipy_direct() c= [0, 3e-4, 2e-2, 5e-2, 1e-2, 1.5e-3, 4e-4, 3e-4, 0] t= [0, 0.3*3600, 0.6*3600, 2*3600, 10*3600, 20*3600, 25*3600, 30*3600, 35*3600] TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f03', 'fract_20')]], sampling_nodes=[bh_nodes[('ki0023b', 'fract_21')]], n_particles=30000, spatial_injection_mode='flux', time_injection_mode='interpolated', c=c, t=t) recovery = TS.RMM.estimate_tracer_recovery() #mycnm.export2vtk('cnm_cacas_flow_cfour') 59

70 TS.set_channel_matrix_models(channels='all', R=1., MPG= e-07) print(recovery) TS.run_particle_tracking() Sparse CNM Leakage scenario transport simulation from pychan3d import Node, Channel, Network, BND_COND, TransportSimulation, DiscreteFractureNetwork, load_network import pickle import numpy as np from copy import copy mycnm.set_channel_apertures() mycnm.solve_steady_state_flow_scipy_direct() TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f02', 'fract_21')]], n_particles=10000, spatial_injection_mode='resident', time_injection_mode='instantaneous', c=none, t=none) recovery = TS.RMM.estimate_tracer_recovery() TS.set_channel_matrix_models(channels='all', R=1., MPG=7.99E-07) #mycnm.export2vtk('cnm_cacas_flow_cthree') print(recovery) TS.run_particle_tracking() Dense CNM Leakage Scenario transport simulation from pychan3d import Node, Channel, Network, BND_COND, TransportSimulation, DiscreteFractureNetwork, load_network import pickle import numpy as np from copy import copy mycnm.solve_steady_state_flow_scipy_direct() TS = TransportSimulation(myCNM, injection_nodes=[bh_nodes[('ki0025f02', 'fract_21')]], n_particles=10000, spatial_injection_mode='resident', time_injection_mode='instantaneous', c=none, t=none) recovery = TS.RMM.estimate_tracer_recovery() TS.set_channel_matrix_models(channels='all', R=1., MPG=7.99E-07) #mycnm.export2vtk('cnm_cacas_flow_cthree') print(recovery) TS.run_particle_tracking() 60

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